In this paper, we define expectation of f∈F, i.e. E(f)=f(?), according to Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we derive a formula for the expectation of ...In this paper, we define expectation of f∈F, i.e. E(f)=f(?), according to Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we derive a formula for the expectation of random Hermite polynomial in Skorohod integral on Guichardet- Fock spaces. In particular, we prove that the anticipative Girsanov identities under the condition E(H<sub>x</sub>(δ(x),‖x‖<sup>2</sup>)),n≥1 on Guichardet-Fock spaces.展开更多
In this paper, we define expectation of f∈E, i.e. E(f)=f(?), accordingto Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we prove a moment identity for the Skorohod ...In this paper, we define expectation of f∈E, i.e. E(f)=f(?), accordingto Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we prove a moment identity for the Skorohod integrals aboutvacuum state.展开更多
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
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
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
In this paper,we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball BX of a complex Banach space X into ℂ.As applications,we will establish refined Bohr...In this paper,we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball BX of a complex Banach space X into ℂ.As applications,we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball BX with values in higher dimensional spaces.Next,we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on BX.In addition,we establish an improved version of the Bohr inequality for holomorphic functions on BX.All the results are proved to be sharp.展开更多
In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[...In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).展开更多
Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) contain...Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.展开更多
In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zer...In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.展开更多
In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for t...In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.展开更多
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
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
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
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
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
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
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
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
文摘In this paper, we define expectation of f∈F, i.e. E(f)=f(?), according to Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we derive a formula for the expectation of random Hermite polynomial in Skorohod integral on Guichardet- Fock spaces. In particular, we prove that the anticipative Girsanov identities under the condition E(H<sub>x</sub>(δ(x),‖x‖<sup>2</sup>)),n≥1 on Guichardet-Fock spaces.
文摘In this paper, we define expectation of f∈E, i.e. E(f)=f(?), accordingto Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we prove a moment identity for the Skorohod integrals aboutvacuum state.
基金Supported by the National Natural Science Foundation of China(11871195)。
文摘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.
基金supported by the NSFC(12301115)the Natural Science Foundation of Huzhou(2023YZ11,2024YZ37)the second author was supported by the NSFC(12071437).
文摘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.
基金supported by the Zhejiang Province Natural Science Foundation of China(LY23A010003).
文摘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<∞).
基金supported by the SERB,SUR/2022/002244,Govt.India and the second author was supported by the UGC-JRF(NTA Ref.No.:201610135853)New Delhi,India,and the third author was partially supported by the JSPS KAKENHI(JP22K03363).
文摘In this paper,we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball BX of a complex Banach space X into ℂ.As applications,we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball BX with values in higher dimensional spaces.Next,we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on BX.In addition,we establish an improved version of the Bohr inequality for holomorphic functions on BX.All the results are proved to be sharp.
基金supported by the Fundamental Research Program of Shanxi Province(202103021223038).
文摘In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).
文摘Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.
基金supported by the National Natural Science Foundation of China(11601525)the Natural Science Foundation of Hunan Province(2024JJ5412),the Changsha Municipal Natural Science Foundation(kq2402193).
文摘In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.
基金Supported by Science and Technology Development Plan Project of Jilin Province China(Grant No.20260102245JC)Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.
基金supported by the China Scholarship Council(Grant No.202306690024)the Ministerio de Ciencia e Innovación and Fondos FEDER(Grant Nos.PID2021-562126509OB-C21 and PDC2022-133332-C21)+1 种基金the Generalitat de Catalunya(Grant No.2021SGR00138)the Beatriu de Pinós Fellowship(Grant No.2021-BP-00206).
文摘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.
文摘文章基于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。
文摘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.
基金Supported by the National Natural Science Foundation of China(12001249)the Natural Science Foundation of Jiangxi Province(20232BAB211004)the Educational Commission Science Programm of Jiangxi Province(GJJ2200523)。
文摘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.
文摘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.
基金Supported in part by NSFC(No.11971005)the Fundamental Research Funds for the Central Universities(Nos.GK202101008,GK202102012)。
文摘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.
基金Supported by Natural Science Foundation of Guangdong Province in China(2018KTSCX161)。
文摘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.
基金Supported by the National Natural Science Foundation of China(12301101)the Guangdong Basic and Applied Basic Research Foundation(2022A1515110019 and 2020A1515110585)。
文摘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.
