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Mixed Quasi-martingale Hardy Spaces
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作者 ZHANG Chuanzhou LI Shimeng HE Zhibin 《应用数学》 北大核心 2026年第1期221-231,共11页
In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale in... In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm. 展开更多
关键词 Mixed quasi-martingale Hardy space Atomic Decomposition σ-sublinear operator
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THE BOUNDEDNESS OF INHOMOGENEOUS CALDERÓN-ZYGMUND CONVOLUTION OPERATORS ON LOCAL PRODUCT HARDY SPACES
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作者 Shaoyong HE Jiecheng CHEN 《Acta Mathematica Scientia》 2026年第1期99-111,共13页
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t... It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense. 展开更多
关键词 local Hardy space Lipschitz space inhomogeneous Calderón-Zygmund operator discrete Calderón identity
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Perturbation Mechanism and Response Measure of Weight Uncertainties on the Optimized Delineation of Production-living-ecological Space:A Case Study of Xuzhou,China
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作者 LI Xin ZHAO Zilong +2 位作者 MA Xiaodong ZHANG Jian XU Haibin 《Chinese Geographical Science》 2025年第4期835-851,共17页
As the core of spatial planning in China,delineation of the production-living-ecological space(PLES)refers to dividing the overall land use into three functional spaces.Spatial units are optimally configured as the mo... As the core of spatial planning in China,delineation of the production-living-ecological space(PLES)refers to dividing the overall land use into three functional spaces.Spatial units are optimally configured as the most suitable functional type,while beset by various uncertainties.Weight uncertainties,being affected by subjective preferences,are highly arbitrary and seriously affect PLES.Taking Xuzhou as the study area,this paper studies the perturbation mechanism and response measure of weight uncertainties on PLES.First,weight samples are obtained through quasi-random sampling to serve as sources of uncertainties for input into the optimized delineation of PLES.Next,the Monte Carlo simulation is applied to simulate the spatial probability distribution of PLES.The global sensitivity analysis method is then adopted to identify the main sources that cause uncertainties in the delineation of PLES.Subsequently,the flexible space(FS)of PLES at a certain level of significance is formulated by comparing the distribution probabilities of spatial units for different functional spaces,acting as a countermeasure for the perturbation.The results show that weight uncertainties bring disturbances to the PLES by affecting the multi-criteria evaluation(MCE)of PLES delineation.The PLES is affected by the weight uncertainties of the factors alone or through interactions with other weights.FS is the spatial response measure of PLES when uncertainties occurred at a certain level of significance.The study introduces the perspective of uncertainty for PLES,which contributes toward improving the scientificity and reliability of PLES. 展开更多
关键词 weight uncertainties optimal delineation production-living-ecological space(PLES) propagation of uncertainties sensitivity analysis flexible space Xuzhou China
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Resilience assessment and obstacle factors of urban production-living-ecological space:A case study of Ganzhou city,China
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作者 TU Xiaoqiang JI Zhengxin +2 位作者 CHEN Hailian LIU Yezhong XU Xiaohua 《Journal of Geographical Sciences》 2025年第4期846-866,共21页
In recent years, the uncontrollable risks of urban production-living-ecological(PLE)space have increased sharply, making resilience enhancement essential for sustainable urban development. Based on the social-ecologic... In recent years, the uncontrollable risks of urban production-living-ecological(PLE)space have increased sharply, making resilience enhancement essential for sustainable urban development. Based on the social-ecological system(SES) theory, this study constructs an assessment framework for urban PLE space resilience by analyzing its inherent characteristics. The central urban area of Ganzhou city is taken as a case study to evaluate urban PLE space resilience and diagnose its obstacles. The results are as follows: The PLE space resilience in the central urban area of Ganzhou exhibits gradations and substantial spatial differentiation. The ecological space resilience in the study area was the highest, followed by that of production space, while living space resilience was the lowest. The primary factors influencing PLE space resilience are concentrated in the dimensions of robustness and adaptability. In particular, the robustness of the PLE space is relatively low. Based on these results, targeted spatial resilience governance strategies for the PLE space have been proposed. These strategies serve as theoretical and technical references for the study area. By adopting the PLE space perspective, this paper enriches resilience research and provide theoretical support for sustainable urban development. 展开更多
关键词 production-living-ecological space urban resilience sustainable development obstacle factors
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Simulation of the future evolution track of“production-living-ecological”space in a coastal city based on multimodel coupling and wetland protection scenarios
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作者 Yitong Yin Rongjin Yang +5 位作者 Zechen Song Yuying Zhang Yanrong Lu Le Zhang Meiying Sun Xiuhong Li 《Geography and Sustainability》 2025年第3期51-63,共13页
Coastal cities hold a special position in the fields of production,living,and ecological research because of their unique wetland resource advantages.However,with global urbanization and rapid economic development,con... Coastal cities hold a special position in the fields of production,living,and ecological research because of their unique wetland resource advantages.However,with global urbanization and rapid economic development,con-flicts among production,living and ecological land are prevalent in coastal cities in the process of maintaining sustainable wetland resources and further developing the social economy.By establishing an SD-PLUS-CCD cou-pling model,this paper analysed the evolution characteristics and driving mechanism of the production-living-ecological space(PLES)and the effects of wetland protection(WLP)on promoting or inhibiting the coordinated development of the PLES in Dongying city during 2005-2060.The results show that(1)from 2005 to 2020,the increase in urban population resulted in a significant transfer of arable land and a reduction of 914 km2 in pro-duction space(PS);(2)from 2020 to 2060,under the WLP scenario,the conversion of wetland ecological space will reduce the PS and living space(LS)by 193.92 km2 and 107.14 km2,respectively,and increase the ecological space(ES)by 327.52 km2;and(3)wetland protection has an inhibitory effect on the coordinated development of PLES in the study area,and the total proportion of noncoordinated areas of PE and living-ecological space will continue to increase during the simulation period.This paper provides a solid theoretical support for the sustain-able management and protection of wetlands in coastal cities and possible PLES conflict patterns and provides a scientific basis for future territorial spatial planning and policy balance analysis. 展开更多
关键词 Wetland protection production-living-ecologicalspace Coupling model Driving mechanism Coordinated and sustainable development
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A GENERALIZED HILBERT OPERATOR ACTING ON HARDY SPACES
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作者 Huiling CHEN Shanli YE 《Acta Mathematica Scientia》 2026年第1期145-163,共19页
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted... Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞). 展开更多
关键词 Hilbert operator Hardy space Carleson measure essential norm
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A Review on the Theory and Principle of the Division of "Production-Living-Ecology" Spaces
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作者 Yongxin WANG Xiaowei SHI Linsen HE 《Asian Agricultural Research》 2025年第7期1-6,共6页
From the concept of the "Production-Living-Ecology" Spaces, this paper sorts out the theoretical basis, division principles, and division methods of the "Production-Living-Ecology" Spaces, and then... From the concept of the "Production-Living-Ecology" Spaces, this paper sorts out the theoretical basis, division principles, and division methods of the "Production-Living-Ecology" Spaces, and then proposes future prospects for them. The integration of theory and practice of "Production-Living-Ecology" Spaces is currently in a stage of in-depth exploration and practical application. Future research should fully recognize the importance and necessity of theoretical research on "Production-Living-Ecology" Spaces under the new situation, and consolidate the theoretical foundation for research on the development and protection of territorial space in the new era. 展开更多
关键词 "production-living-ecology"spaces Division methods Territorial spatial planning Ecological priority
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Characteristics and influencing mechanisms of production-living-ecological space dynamics in the Three Gorges Reservoir Area(TGRA),Chongqing,China 被引量:1
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作者 ZHU Xinyi GAO Jinlong 《Regional Sustainability》 2024年第2期49-62,共14页
The Three Gorges Reservoir Area(TGRA)is an important ecological barrier in the Yangtze River Basin,China.Therefore,it is of great importance to understand the spatio-temporal variation and the driving factors of produ... The Three Gorges Reservoir Area(TGRA)is an important ecological barrier in the Yangtze River Basin,China.Therefore,it is of great importance to understand the spatio-temporal variation and the driving factors of production-living-ecological spaces for sustainable and high-quality development in the TGRA.This study investigated the dynamic variation of production-living-ecological spaces in the TGRA by employing land use data in 2000,2005,2010,2015,and 2018,and detected the influencing factors by using the Geographic detector(GeoDetector).Results implied that the structure and dynamic trajectories of production-living-ecological spaces in the TGRA varied in both horizontal and vertical directions,and the study area was dominated by ecological space.A spatial orientation towards the northeast was detected in the evolution of production-living-ecological spaces during 2000-2018.In terms of quantity,the transition from ecological space(grassland and woodland)to agriculture land accounted for the largest proportion from 2000 to 2018.However,the reverse transition from agriculture land to ecological space has increased since 2000 with the efforts of“Grain for Green”.In terms of temporal scale,there was a fluctuating trend in production space with the continuous expansion of living space,while ecological space showed an inverted U-shaped trend during 2000-2018.The dynamic pattern of production-living-ecological spaces in the TGRA was influenced by both physical and socio-economic variables as basic determinants and dominant driving factors,respectively.Finally,the harmonization and protection of production-living-ecological spaces still require policy-makers’efforts.This work may have potential in advancing our understanding about land use conflicts,and provide a reference for rational layout of spatial functions and the realization of sustainable development in the TGRA. 展开更多
关键词 production-living-ecological spaces Functional transition Three Gorges Reservoir Area(TGRA) Physical and socio-economic variables Yangtze River
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Ecological function transitions of land use in the Beibu Gulf Economic Zone from the perspective of production-living-ecological space
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作者 ZHOU Guipeng LONG Hualou +1 位作者 JIANG Yanfeng TU Shuangshuang 《Journal of Geographical Sciences》 SCIE CSCD 2024年第11期2212-2238,共27页
The ecological function of land use is the basis for developing an ecological civilization and realizing sustainable development.This paper may help guide the coordination of economic development and ecological develo... The ecological function of land use is the basis for developing an ecological civilization and realizing sustainable development.This paper may help guide the coordination of economic development and ecological development in China’s coastal border areas.Based on theoretical analysis,this paper studies the spatiotemporal evolution of the functional spaces and the ecological function transitions of land use in the Beibu Gulf Economic Zone(BGEZ)by analyzing patterns,processes,and factors by applying eco-environmental quality index,grid subdivision,kriging interpolation,barycenter model,and Geodetector.This paper constructs a theoretical framework of ecological function transitions of land use based on the research idea of“system-pattern-process-factor”,and carries out empirical research.Some conclusions can be drawn as follows:(1)The ecological space in the BGEZ has continuously decreased,converting mainly into agricultural production space and industrial-mining production space.The production space has expanded slowly.The area of living space in the BGEZ has increased rapidly.(2)The ecological function of land use in the BGEZ has continued to weaken,especially in the southern part of the BGEZ.The“high-sub-high”quality zones of ecological function are retreating to the north.(3)There were more deterioration transition areas than optimization transition areas of ecological function in the BGEZ.The former were mostly located in the central and southern urbanized areas of the BGEZ,whereas the latter were mostly located in the edge zones of district and county units.(4)As for the driving factors of the deterioration transitions of land use ecological function in the BGEZ,the significant trend of“de-ecologization”of the land cover/land use structure was the dominant driving factor;the interactions among the“natural-socioeconomic-managerial”systems were the main recessive factor.The natural system played a fundamental role,and the driving force of natural factors was the strongest.The industrialization,urbanization,and GDP increment in the socioeconomic system and the policy positioning of development intensity in the managerial system played a significant role.The interactions among natural factors,road construction,and industrial non-agricultural transformation had a“fuze”effect on stimulating driving forces. 展开更多
关键词 land use transitions ecological function eco-environmental quality production-living-ecological spaces dominant and recessive factors Beibu Gulf
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基于Space P和K-means的货运航司航线网络特征分析研究
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作者 罗凤娥 卫昌波 +1 位作者 韩晓彤 郭玲玉 《现代电子技术》 北大核心 2026年第1期102-107,共6页
针对航空货运行业的迅速扩张,航空货运网络结构变得更加复杂,文中通过Space P建模方法构建了货运航空公司航线网络模型,并运用K-means聚类算法对网络进行了深入分析。选取度、平均路径长度、聚类系数和中间度等关键网络特性指标对航线... 针对航空货运行业的迅速扩张,航空货运网络结构变得更加复杂,文中通过Space P建模方法构建了货运航空公司航线网络模型,并运用K-means聚类算法对网络进行了深入分析。选取度、平均路径长度、聚类系数和中间度等关键网络特性指标对航线网络进行层次化分类,揭示了网络的复杂特征和层次结构。通过仿真实验评估了网络的小世界特性,并利用轮廓系数得到不同K值下的聚类结果,进而确定最优聚类结果。同时,模拟了航线网络在遭受攻击时的鲁棒性,实验结果表明:在航线网络较为脆弱的情况下,该方法为货运航司航线网络的优化和抗风险能力的提升提供了重要参考。 展开更多
关键词 航空货运 space P 航线网络 复杂网络 聚类算法 网络特征
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Enhanced characterization of depolarizing samples using indices of polarization purity and polarizance–reflection–transformation spaces 被引量:1
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作者 Dekui Li Ivan Montes +5 位作者 Mónica Canabal-Carbia Irene Estévez Octavi Lopez-Coronado Zhongyi Guo Juan Campos Ángel Lizana 《Advanced Photonics Nexus》 2025年第1期77-92,共16页
Depolarizing behavior is commonly observed in most natural samples.For this reason,optical tools measuring the differences in depolarization response among spatially separated structures are highly useful in a wide ra... Depolarizing behavior is commonly observed in most natural samples.For this reason,optical tools measuring the differences in depolarization response among spatially separated structures are highly useful in a wide range of imaging applications for enhanced visualization of structures,target identification,etc.One commonly used tool for depolarizing discrimination is the so-called depolarizing spaces.In this article,we exploit the combined use of two depolarizing spaces,the indices of polarization purity(IPP)and polarizance–reflection–transformation(PRT)spaces,to improve the capability of optical systems to identify polarization–anisotropy depolarizers.The potential of these spaces to discriminate among different depolarizers is first studied from a series of simulations by incoherently adding diattenuations or retarders,with some control parameters emulating samples in nature.The simulated results demonstrate that the proposed methods are capable of increasing differences among depolarizers beyond other well-known techniques.Experimentally,validation is provided by conducting diverse phantom experiments of easy interpretation and mimicking the stated simulations.As a useful application of our approach,we developed a model able to retrieve intrinsic microscopic information of samples from macroscopic polarimetric measurements.The proposed methods enable non-invasive,straightforward,macroscopic characterization of depolarizing samples,and may be of interest for enhanced visualization of samples in multiple imaging scenarios. 展开更多
关键词 DEPOLARIZER RETARDER diattenuator polarization space.
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近二十年国内外图书馆学习空间研究的比较分析——基于Citespace和Bicomb的可视化计量分析
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作者 诸葛晴怡 《建筑与文化》 2026年第2期165-168,共4页
文章基于CNKI、Web of Science两大数据库2005—2024年收录的图书馆学习空间研究文献,运用CiteSpace、Bicomb、SPSS软件进行可视化分析。结果显示,国外研究以技术驱动创新为主导,聚焦智能化技术与跨学科应用;而国内研究呈现理论创新与... 文章基于CNKI、Web of Science两大数据库2005—2024年收录的图书馆学习空间研究文献,运用CiteSpace、Bicomb、SPSS软件进行可视化分析。结果显示,国外研究以技术驱动创新为主导,聚焦智能化技术与跨学科应用;而国内研究呈现理论创新与实践探索并重,通过大数据、AI等技术形成本土化解决方案。文章提出通过数字技术与人文关怀的平衡发展、国际化视野与本土化创新的有机结合、理论研究与实践应用的深度融合,为我国图书馆学习空间的研究提供借鉴与参考。 展开更多
关键词 图书馆学习空间 知识图谱 可视化分析 比较分析
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Integration of Regional Culture into the Landscape Design of Rural Public Spaces:A Case Study of Xiaomaopoying Village in Enshi 被引量:1
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作者 HE Minghao 《Journal of Landscape Research》 2025年第2期47-50,共4页
In the context of rural revitalization,the landscape design of public spaces in Enshi Xiaomaopoying Village presents both new opportunities and challenges.This study explores the significance of integrating regional c... In the context of rural revitalization,the landscape design of public spaces in Enshi Xiaomaopoying Village presents both new opportunities and challenges.This study explores the significance of integrating regional culture into rural public spaces.Field research has been conducted to assess the current utilization of regional culture in the public spaces of Xiaomaopoying Village.Subsequently,design optimization strategies are analyzed and proposed.Additionally,the practical application of regional cultural elements is examined,in order to offer guidance for the application of cultural creation of traditional characteristic villages in rural public spaces. 展开更多
关键词 Xiaomaopoying Village MIAO Rural public space Regional culture Landscape design
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An Evaluation System for Agriculture and Tourism Coupling Degree of Rural Complex Based on Production-living-ecological Space
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作者 Yan WANG Keying LINGHU +3 位作者 Yiwei FENG Jingyi YANG Chang ZHONG Junyi WEI 《Asian Agricultural Research》 2020年第9期65-69,72,共6页
Rural complex is a bright spot for China to realize the development of new industries for rural revitalization.Starting from the concept,development history and current situation of rural complex,based on the perspect... Rural complex is a bright spot for China to realize the development of new industries for rural revitalization.Starting from the concept,development history and current situation of rural complex,based on the perspective of production-living-ecological space,according to the different characteristics of agriculture and tourism,3 secondary indices and 18 tertiary indices were selected,and each of them was weighted using the Delphi expert consultation method and analytic hierarchy process(AHP)to construct an evaluation system for the coupling degree of agriculture and tourism in rural complex.The results show gross domestic product and forest coverage have the most significant impact on agriculture,economic benefits and the ecological water quality of tourist attractions have the most significant impact on the tourism industry,and tourism economic benefits and agricultural ecological benefits have the most significant impact on rural complex. 展开更多
关键词 Rural revitalization production-living-ecological space AGRICULTURE Tourism Rural complex Agriculture and tourism coupling Evaluation system Analytic hierarchy process(AHP)
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Coincidence Point and Common Fixed Point Theorems on b-Metric-like Spaces
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作者 LUO Ting 《应用数学》 北大核心 2025年第3期831-840,共10页
In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main re... In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main results generalize and extend several well-known comparable results from the existing literature.Moreover,some examples are provided to illustrate the main results. 展开更多
关键词 b-metric-like space Partially ordered b-metric-like space Expansive mapping f-weakly isotone mapping Coincidence point Common fixed point
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A Note for Weighted Local Hardy Spaces
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作者 ZHAO Haijing LI Baode 《数学进展》 北大核心 2025年第5期1095-1101,共7页
Inhomogeneous Calderon-Zygmund operator T maps each atom into an approximate molecule of weighted local Hardy space if and only if some approximate cancellation condition holds for T.An equivalent norm for weighted Le... Inhomogeneous Calderon-Zygmund operator T maps each atom into an approximate molecule of weighted local Hardy space if and only if some approximate cancellation condition holds for T.An equivalent norm for weighted Lebesgue space which has vanishing moments up to order s plays an important role,where s∈N. 展开更多
关键词 local Hardy space Calderon-Zygmund operator Muckenhoupt weight
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The Minimal Affine Total Variation in Minkowski Spaces
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作者 MOU Shuang 《数学进展》 北大核心 2025年第1期164-176,共13页
In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total vari... In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space. 展开更多
关键词 convex body minimal surface area Minkowski space bounded variation
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Products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball
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作者 ZHANG Chao QIN Yuehai 《中山大学学报(自然科学版)(中英文)》 北大核心 2025年第2期160-169,共10页
The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic fu... The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results. 展开更多
关键词 composition operator multiplication operator differentiation operator weighted Bergman space
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The Paley-Wiener Theorem for General Weighted Hardy Spaces on Tube Domains
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作者 HUANG Yun ZHANG Dawei 《应用数学》 北大核心 2025年第3期841-849,共9页
In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequen... In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights. 展开更多
关键词 Paley-Wiener Theorem Fourier transform Weighted Hardy space Tube domain
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Boundedness of the Commutators of Rough Singular Integral Operators on Triebel–Lizorkin Spaces
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作者 LIU Jie GAO Wenhua 《数学进展》 北大核心 2025年第5期1075-1086,共12页
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(... Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β. 展开更多
关键词 rough singular integral operator COMMUTATOR Triebel-Lizorkin space Littlewood-Paley theory
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