In this paper, we give the four equivalent characterizations for the weighted local hardy spaces on Lipschitz domains. Also, we give their application for the harmonic function defined in bounded Lipschitz domains.
Decreasing of layer thickness causes the decrease of polarization until it disappears due to the existence of depolarization field.Therefore,the search for strong piezoelectric materials is highly desirable for multif...Decreasing of layer thickness causes the decrease of polarization until it disappears due to the existence of depolarization field.Therefore,the search for strong piezoelectric materials is highly desirable for multifunctional ultra-thin piezoelectric devices.Herein,we propose a common strategy for achieving strong piezoelectric materials through the electronic asymmetry induced by the intrinsically asymmetric atomic character of different chalcogen atoms.Accordingly,in the tetrahedral lattice structures,for example,M4X3Y3(M=Pd/Ni,X/Y=S,Se or Te,X≠Y)monolayers are proved to display excellent out-of-plane piezoelectricity.Ni4Se3Te3 possesses the largest piezoelectric coefficient d33 of 61.57 pm/V,which is much larger than that of most 2D materials.Enhancing the electronic asymmetry further increases the out-of-plane piezoelectricity of Janus M4X3Y3 materials.Correspondingly,the out-of-plane piezoelectricity is positively correlated with the ratio of electronegativity difference(Red)and the electric dipole moment(P).This work provides alternative materials for energy harvesting nano-devices or self-energized wearable devices,and supplies a valuable guideline for predicting 2D materials with strong out-of-plane piezoelectricity.展开更多
Musielak-Orlicz-Lorentz Hardy Spaces:Maximal Function, Finite Atomic, and Littlewood—Paley Characterizations with Applications to Dual Spaces and Summability of Fourier Transforms Hongchao Jia Der-Chen Chang Ferenc W...Musielak-Orlicz-Lorentz Hardy Spaces:Maximal Function, Finite Atomic, and Littlewood—Paley Characterizations with Applications to Dual Spaces and Summability of Fourier Transforms Hongchao Jia Der-Chen Chang Ferenc Weisz Dachun Yang Wen Yuan Abstract Let q ∈ (0, ∞] and φ be a Musielak-Orlicz function with uniformly lower type pφ-∈(0, ∞) and uniformly upper type pφ+∈(0, ∞). In this article, the authors establish various realvariable characterizations of the Musielak-Orlicz-Lorentz Hardy space Hφ,q(R^(n)),respectively,in terms of various maximal functions, finite atoms, and various Littlewood-Paley functions.展开更多
Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As ...Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As an application,we prove that the dual space of H x(Rn)is the Campanato space associated with X.For any given a∈(0,1]and s∈Z+,using the atomic and the Littlewood—Paley function characterizations of H x(Rn),we also establish its 5-order intrinsic square function characterizations,respectively,in terms of the intrinsic Lusin-area function S a,s,the intrinsic g-function g a,s,and the intrinsic g*λ-function g*λ,a,s,whereλcoincides with the best known range.展开更多
Transmission electron microscopy(TEM)is an indispensable tool for elucidating the intrinsic atomic structures of materials and provides deep insights into defect dynamics,phase transitions,and nanoscale structural det...Transmission electron microscopy(TEM)is an indispensable tool for elucidating the intrinsic atomic structures of materials and provides deep insights into defect dynamics,phase transitions,and nanoscale structural details.While numerous intriguing physical properties have been revealed in recently discovered two-dimensional(2D)quantummaterials,many exhibit significant sensitivity towater and oxygen under ambient conditions.This inherent instability complicates sample preparation for TEM analysis and hinders accurate property measurements.This review highlights recent technical advancements to preserve the intrinsic structures of water-and oxygen-sensitive 2D materials for atomic-scale characterizations.A critical development discussed in this review is implementing an inert gas-protected glovebox integrated system(GIS)designed specifically for TEM experiments.In addition,this review emphasizes air-sensitivematerials such as 2D transitionmetal dichalcogenides,transition metal dihalides and trihalides,and low-dimensional magnetic materials,demonstrating breakthroughs in overcoming their environmental sensitivity.Furthermore,the progress in TEM characterization enabled by the GIS is analyzed to provide a comprehensive overview of state-of-the-art methodologies in this rapidly advancing field.展开更多
In this paper, we study the boundedness of the Hausdorff operator H_? on the real line R. First, we start with an easy case by establishing the boundedness of the Hausdorff operator on the Lebesgue space L^p(R)and the...In this paper, we study the boundedness of the Hausdorff operator H_? on the real line R. First, we start with an easy case by establishing the boundedness of the Hausdorff operator on the Lebesgue space L^p(R)and the Hardy space H^1(R). The key idea is to reformulate H_? as a Calder′on-Zygmund convolution operator,from which its boundedness is proved by verifying the Hrmander condition of the convolution kernel. Secondly,to prove the boundedness on the Hardy space H^p(R) with 0 < p < 1, we rewrite the Hausdorff operator as a singular integral operator with the non-convolution kernel. This novel reformulation, in combination with the Taibleson-Weiss molecular characterization of H^p(R) spaces, enables us to obtain the desired results. Those results significantly extend the known boundedness of the Hausdorff operator on H^1(R).展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10377108)the Natural Science Foundation of Guangdong Province (No. 031495), China
文摘In this paper, we give the four equivalent characterizations for the weighted local hardy spaces on Lipschitz domains. Also, we give their application for the harmonic function defined in bounded Lipschitz domains.
基金the National Natural Science Foundation of China(Grant No.11474123).
文摘Decreasing of layer thickness causes the decrease of polarization until it disappears due to the existence of depolarization field.Therefore,the search for strong piezoelectric materials is highly desirable for multifunctional ultra-thin piezoelectric devices.Herein,we propose a common strategy for achieving strong piezoelectric materials through the electronic asymmetry induced by the intrinsically asymmetric atomic character of different chalcogen atoms.Accordingly,in the tetrahedral lattice structures,for example,M4X3Y3(M=Pd/Ni,X/Y=S,Se or Te,X≠Y)monolayers are proved to display excellent out-of-plane piezoelectricity.Ni4Se3Te3 possesses the largest piezoelectric coefficient d33 of 61.57 pm/V,which is much larger than that of most 2D materials.Enhancing the electronic asymmetry further increases the out-of-plane piezoelectricity of Janus M4X3Y3 materials.Correspondingly,the out-of-plane piezoelectricity is positively correlated with the ratio of electronegativity difference(Red)and the electric dipole moment(P).This work provides alternative materials for energy harvesting nano-devices or self-energized wearable devices,and supplies a valuable guideline for predicting 2D materials with strong out-of-plane piezoelectricity.
文摘Musielak-Orlicz-Lorentz Hardy Spaces:Maximal Function, Finite Atomic, and Littlewood—Paley Characterizations with Applications to Dual Spaces and Summability of Fourier Transforms Hongchao Jia Der-Chen Chang Ferenc Weisz Dachun Yang Wen Yuan Abstract Let q ∈ (0, ∞] and φ be a Musielak-Orlicz function with uniformly lower type pφ-∈(0, ∞) and uniformly upper type pφ+∈(0, ∞). In this article, the authors establish various realvariable characterizations of the Musielak-Orlicz-Lorentz Hardy space Hφ,q(R^(n)),respectively,in terms of various maximal functions, finite atoms, and various Littlewood-Paley functions.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11971058,11761131002,11671185,11871100).
文摘Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As an application,we prove that the dual space of H x(Rn)is the Campanato space associated with X.For any given a∈(0,1]and s∈Z+,using the atomic and the Littlewood—Paley function characterizations of H x(Rn),we also establish its 5-order intrinsic square function characterizations,respectively,in terms of the intrinsic Lusin-area function S a,s,the intrinsic g-function g a,s,and the intrinsic g*λ-function g*λ,a,s,whereλcoincides with the best known range.
基金supported by the National Key Basic Research and Development Program of China,China(No.2024YFA1409100)support by the National Natural Science Foundation of China,China(Nos.52473302 and 12461160252)+4 种基金Guangdong Innovative and Entrepreneurial Research Team Program,China(No.2019ZT08C044)Guangdong Basic Science Foundation,China(2023B1515120039)Shenzhen Science and Technology Program,China(No.20200925161102001)the Science,Technology and Innovation Commission of Shenzhen Municipality,China(No.ZDSYS20190902092905285)Quantum Science Strategic Special Project from the Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area,China(No.GDZX2301006).
文摘Transmission electron microscopy(TEM)is an indispensable tool for elucidating the intrinsic atomic structures of materials and provides deep insights into defect dynamics,phase transitions,and nanoscale structural details.While numerous intriguing physical properties have been revealed in recently discovered two-dimensional(2D)quantummaterials,many exhibit significant sensitivity towater and oxygen under ambient conditions.This inherent instability complicates sample preparation for TEM analysis and hinders accurate property measurements.This review highlights recent technical advancements to preserve the intrinsic structures of water-and oxygen-sensitive 2D materials for atomic-scale characterizations.A critical development discussed in this review is implementing an inert gas-protected glovebox integrated system(GIS)designed specifically for TEM experiments.In addition,this review emphasizes air-sensitivematerials such as 2D transitionmetal dichalcogenides,transition metal dihalides and trihalides,and low-dimensional magnetic materials,demonstrating breakthroughs in overcoming their environmental sensitivity.Furthermore,the progress in TEM characterization enabled by the GIS is analyzed to provide a comprehensive overview of state-of-the-art methodologies in this rapidly advancing field.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671363, 11471288 and 11601456)
文摘In this paper, we study the boundedness of the Hausdorff operator H_? on the real line R. First, we start with an easy case by establishing the boundedness of the Hausdorff operator on the Lebesgue space L^p(R)and the Hardy space H^1(R). The key idea is to reformulate H_? as a Calder′on-Zygmund convolution operator,from which its boundedness is proved by verifying the Hrmander condition of the convolution kernel. Secondly,to prove the boundedness on the Hardy space H^p(R) with 0 < p < 1, we rewrite the Hausdorff operator as a singular integral operator with the non-convolution kernel. This novel reformulation, in combination with the Taibleson-Weiss molecular characterization of H^p(R) spaces, enables us to obtain the desired results. Those results significantly extend the known boundedness of the Hausdorff operator on H^1(R).
