The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle ...The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).展开更多
The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this arti...The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.展开更多
We study complex interpolation of weighted Besov and Lizorkin–Triebel spaces.The used weights w0,w1 are local Muckenhoupt weights in the sense of Rychkov.As a first step we calculate the Calder′on products of associ...We study complex interpolation of weighted Besov and Lizorkin–Triebel spaces.The used weights w0,w1 are local Muckenhoupt weights in the sense of Rychkov.As a first step we calculate the Calder′on products of associated sequence spaces.Finally,as a corollary of these investigations,we obtain results on complex interpolation of radial subspaces of Besov and Lizorkin–Triebel spaces on Rd.展开更多
In this article,we discuss the complex interpolation of various closed subspaces of Morrey spaces.We have been considering some closed subspaces of Morrey spaces in our earlier works.The main property that we need is ...In this article,we discuss the complex interpolation of various closed subspaces of Morrey spaces.We have been considering some closed subspaces of Morrey spaces in our earlier works.The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al.(2015),it seems to be natural to consider the convolution property as well.Our result will extend the results by Hakim and Sawano(2017)and Hakim et al.(2017).展开更多
We prove that the inner complex interpolation of two quasi-Banach lattices coincides with the closure of their intersection in their Calderon product. This generalizes a classical result by V. A. Shestakov in 1974 for...We prove that the inner complex interpolation of two quasi-Banach lattices coincides with the closure of their intersection in their Calderon product. This generalizes a classical result by V. A. Shestakov in 1974 for Banach lattices.展开更多
In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
Let S∞ denote the unit sphere in some infinite dimensional complex Hilbert space (H,<·,·>)Let z1,z2,…,z1 be distinct points on S∞ This paper deals with interpolation of arbitrary data on the zj by a...Let S∞ denote the unit sphere in some infinite dimensional complex Hilbert space (H,<·,·>)Let z1,z2,…,z1 be distinct points on S∞ This paper deals with interpolation of arbitrary data on the zj by a function in the linear span of the l functionswhen is a suitable function that operates on nonnegative definite matrices.Conditions for the strict positive definiteness of the kernel are obtained.展开更多
This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.
Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates...Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ.展开更多
The weak-type (1, 1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We discuss a pol...The weak-type (1, 1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We discuss a polynomial weight w that makes the Riesz-Laguerre transforms of order greater than or equal to 2 continuous from L<sup>1</sup> (wdμ<sub>α</sub>) into L<sup>1,∞</sup> (dμ<sub>α</sub>), under specific value α, where μα</sub> is the Laguerre measure.展开更多
Electric load movement forecast is increasingly importance for the industry.This study addresses the load movement forecast modeling based on complex matrix interpolation of the S-transform(ST).In complex matrix of ti...Electric load movement forecast is increasingly importance for the industry.This study addresses the load movement forecast modeling based on complex matrix interpolation of the S-transform(ST).In complex matrix of time-frequency representation of the ST,each row follows conjugate symmetric property and each column appears a certain degree of similarity.Based on these characteristics,a complex matrix interpolation method for the time-frequency representation of the ST is proposed to interpolate each row of the complex matrix based on the conjugate symmetric property,and then to perform nearestneighbor interpolation on each column.Then with periodic extension for daily and yearly electric load movement,a forecast model employing the complex matrix interpolation of the ST is introduced.The forecast approach is applied to predict daily load movement of the European Network on Intelligent Technologies(EUNITE)load dataset and annual electric load movement of State Gird Corporation of China and its branches in 2005 and 2006.Result analysis indicates workability and effectiveness of the proposed method.展开更多
We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method,...We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.展开更多
In this paper, linear combinations of composition operators acting on weighted Dirichlet spaces are studied. By using the first derivative of the kernel function, we obtain a lower estimate for the essential norms of ...In this paper, linear combinations of composition operators acting on weighted Dirichlet spaces are studied. By using the first derivative of the kernel function, we obtain a lower estimate for the essential norms of these operators acting on the Dirichlet space D and S2. For general weighted Dirichlet space, by using complex interpolation methods, we characterize the compactness of these operators induced by linear fractional self-maps of the disk.展开更多
基金supported by the Innovation Research for the Postgrad-uates of Guangzhou University(2020GDJC-D06)supported by the National Natural Science Foundation of China(12071229)。
文摘The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).
基金Supported by NSF of Henan Province of China(20001110001)
文摘The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.
基金Supported by the DFG Research Center Matheon"Mathematics for key technologies"in Berlin
文摘We study complex interpolation of weighted Besov and Lizorkin–Triebel spaces.The used weights w0,w1 are local Muckenhoupt weights in the sense of Rychkov.As a first step we calculate the Calder′on products of associated sequence spaces.Finally,as a corollary of these investigations,we obtain results on complex interpolation of radial subspaces of Besov and Lizorkin–Triebel spaces on Rd.
基金supported by Grant-in-Aid for Scientific Research(C)(Grant No.16K05209)Japan Society for the Promotion of Science and Department of Mathematics Analysis and the Theory of FunctionsPeoples’Friendship University of Russia。
文摘In this article,we discuss the complex interpolation of various closed subspaces of Morrey spaces.We have been considering some closed subspaces of Morrey spaces in our earlier works.The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al.(2015),it seems to be natural to consider the convolution property as well.Our result will extend the results by Hakim and Sawano(2017)and Hakim et al.(2017).
文摘We prove that the inner complex interpolation of two quasi-Banach lattices coincides with the closure of their intersection in their Calderon product. This generalizes a classical result by V. A. Shestakov in 1974 for Banach lattices.
文摘In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
文摘Let S∞ denote the unit sphere in some infinite dimensional complex Hilbert space (H,<·,·>)Let z1,z2,…,z1 be distinct points on S∞ This paper deals with interpolation of arbitrary data on the zj by a function in the linear span of the l functionswhen is a suitable function that operates on nonnegative definite matrices.Conditions for the strict positive definiteness of the kernel are obtained.
基金supported by the National Natural Science Foundation of China(11171027and 11101038)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20120003110003)+1 种基金the Fundamental Research Funds for Central Universities of China(2012LYB26)supported by the Alexander von Humboldt Foundation
文摘This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.
基金Supported by Natural Science Fundation of Anhui Province (07021019)Education Committee of AnhuiProvince (KJ2007A009 KJ2008B244)
文摘Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ.
文摘The weak-type (1, 1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We discuss a polynomial weight w that makes the Riesz-Laguerre transforms of order greater than or equal to 2 continuous from L<sup>1</sup> (wdμ<sub>α</sub>) into L<sup>1,∞</sup> (dμ<sub>α</sub>), under specific value α, where μα</sub> is the Laguerre measure.
基金supported by the Scientific Research Fund of Hunan Provin-cial Science and Technology Department(2013GK3090)the research fund of Hunan University of Science and Technology(E50811)。
文摘Electric load movement forecast is increasingly importance for the industry.This study addresses the load movement forecast modeling based on complex matrix interpolation of the S-transform(ST).In complex matrix of time-frequency representation of the ST,each row follows conjugate symmetric property and each column appears a certain degree of similarity.Based on these characteristics,a complex matrix interpolation method for the time-frequency representation of the ST is proposed to interpolate each row of the complex matrix based on the conjugate symmetric property,and then to perform nearestneighbor interpolation on each column.Then with periodic extension for daily and yearly electric load movement,a forecast model employing the complex matrix interpolation of the ST is introduced.The forecast approach is applied to predict daily load movement of the European Network on Intelligent Technologies(EUNITE)load dataset and annual electric load movement of State Gird Corporation of China and its branches in 2005 and 2006.Result analysis indicates workability and effectiveness of the proposed method.
基金supported by National Natural Science Foundation of China(Grant Nos.11471042,11171027 and 11361020)the Alexander von Humboldt Foundation+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2013YB60 and 2014KJJCA10)
文摘We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.
文摘In this paper, linear combinations of composition operators acting on weighted Dirichlet spaces are studied. By using the first derivative of the kernel function, we obtain a lower estimate for the essential norms of these operators acting on the Dirichlet space D and S2. For general weighted Dirichlet space, by using complex interpolation methods, we characterize the compactness of these operators induced by linear fractional self-maps of the disk.
