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相关于算子的Orlicz-型函数空间的实变理论
  • 项目名称：相关于算子的Orlicz-型函数空间的实变理论
  • 项目类别：面上项目
  • 批准号：11171027
  • 申请代码：A010504
  • 项目来源：国家自然科学基金
  • 研究期限：2012-01-01-2015-12-31
  • 项目负责人：杨大春
  • 负责人职称：教授
  • 依托单位：北京师范大学
  • 批准年度：2011
中文摘要：

数学与物理中的许多重要问题均可归结为算子在某些函数空间的有界性,而刻画这些算子的有界性离不开相应函数空间的实变理论.申请人及其合作者已建立了相关于欧氏空间上二阶散度型椭圆算子或Schr?dinger算子的Orlicz-Hardy空间和具有多项式增长非倍测度欧氏空间上包括Hardy空间等在内的某些函数空间的实变理论，并已将其应用于相关的Riesz算子或奇异积分算子有界性的研究中.本课题拟进一步建立欧氏空间及其区域上相关于高阶散度型椭圆算子或高阶Schr?dinger型算子、及以具有多项式增长非倍测度欧氏空间和齐型空间为其特例的非齐型空间上包括Hardy空间在内的Orlicz型函数空间的实变特征,其中包括这些空间的原子、分子分解特征,各种极大函数特征,Littlewood-Paley函数特征等;并将其应用于相关的Riesz算子、分数次积分、谱乘子及Bergman型奇异积分等算子有界性的研究中.

中文主题词： 算子；函数空间；实变理论；欧氏空间；非齐型空间
英文摘要：

operator；function space；real-variable theory；Euclidean space；space of non-homgeneous type

英文主题词： operator；function space；real-variable theory；Euclidean space；space of non-homgeneous type
结论摘要：

数学和物理中的许多重要问题均可归结为算子在某些函数空间的有界性，而刻画这些算子的有界性离不开相应函数空间的实变理论. 本项目系统地发展了欧氏空间上Musielak-Orlicz型Hardy空间的实变理论, 包括径向与非切向极大函数刻画、分子特征和(内蕴)平方函数刻画. 在欧氏空间上引入了Musielak-Orlicz-Campanato空间, 并证明了其为Musielak-Orlicz型Hardy空间的对偶空间. 研究了欧氏空间上Besov-Triebel-Lizorkin型空间的新的实变特征, 包括平方函数刻画, 复插值, 嵌入性质, 前对偶理论等. 在欧式空间上, 引入了带变指标的Besov型和Triebel-Lizorkin型空间, 建立了其原子分解和Peetre极大函数等实变特征; 作为应用, 得到了其上的一个迹定理. 在欧式空间, 强Lipschitz区域和齐型空间上, 建立了与算子(包括有界解析泛函演算和k-Davies-Gaffney估计的1-1角型算子, 具有非负局部可积位势的带磁场的Schr？dinger算子, 有高斯性质的散度型椭圆算子)相关的Musielak-Orlicz型Hardy空间的实变理论, 并应用于研究Riesz变换的有界性和端点的弱有界性. 在度量测度空间上, 建立了Morrey型空间上包括算子有界性、插值定理以及点态乘子刻画在内的实变理论, 研究了Newton型Besov-Triebel-Lizorkin空间和Hajlasz-Sobolev空间上的实变理论. 在非齐型空间上引入了原子Hardy空间和分子Hardy空间, 建立了它们的对偶理论, 并研究了Calderón-Zygmund算子在其上的有界性.

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 91
  • 0
  • 0
  • 0
  • 1
期刊论文
Boundedness of Calderón-Zygmund operators on non-homogeneous metric measure spaces: equivalent chara
Maximal function characterizations of Hardy spaces associated with magnetic Schr？dinger operators
Dyadic sets, maximal functions and applications on ax plus b-groups
Hardy spaces associated with magnetic Schr？dinger operators on strongly Lipschitz domains
BOUNDEDNESS OF MULTILINEAR COMMUTATORS OF CALDERóN-ZYGMUND OPERATORS ON ORLICZ SPACES OVER NON-HOMOG
New real-variable characterizations of Musielak-Orlicz Hardy spaces
Duality of weighted anisotropic Besov and Triebel-Lizorkin spaces
Hardy spaces (HLRn)-R-p) associated with operators satisfying k-Davies-Gaffney estimates
Continuity of solutions to n-harmonic equations
Local Hardy spaces of Musielak-Orlicz type and their applications
Boundedness of Calderón-Zygmund Operators on Non-homogeneous Metric Measure Spaces
Real-variable characterizations of Orlicz-Hardy spaces on strongly Lipschitz domains of Rn
Real-variable characterizations of Orlicz-Hardy spaces on strongly Lipschitz domains of R-n
Musielak-Orlicz Campanato spaces and applications
Function spaces of Besov-type and Triebel-Lizorkin-Type -- a survey
The grand Lusin-area characterization of Hajlasz-Sobolev spaces and Triebel-Lizorkin spaces
Endpoint boundedness of Riesz transforms on Hardy spaces associated with operators
Boundedness of Calderón-Zygmund operators with finite non-doubling measures
Orlicz-Hardy Spaces Associated with Divergence Operators on Unbounded Strongly Lipschitz Domains of
Lusin area function and molecular characterizations of Musielak-Orlicz Hardy spaces and their applic
Weighted local Orlicz-Hardy spaces on domains and their applications in inhomogeneous dirichlet and
Weighted Hardy spaces associated with operators satisfying reinforced off-diagonal estimates
Complex interpolation on Besov-type and Triebel-Lizorkin-type spaces
Atomic decompositions of Triebel-Lizorkin spaces with local weights and applications
Limiting embeddings in smoothness Morrey spaces, continuity envelopes and applications
Hajlasz gradients are upper gradients
Characterizations of Sobolev spaces via averages on balls
Musielak-Orlicz BMO-type Spaces Associated with Generalized Approximations to the Identity
Musielak-Orlicz-Hardy Spaces Associated with Operators and Their Applications
Estimates for second-order Riesz transforms associated with magnetic Schr？dinger operators on Musiel
Pointwise multipliers for localized morrey-campanato spaces on RD-spaces
Boundedness of intrinsic littlewood-paley functions on musielak-orlicz morrey and campanato spaces
Compact embeddings of radial and subradial subspaces of some Besov-type spaces related to Morrey spa
Boundedness of Generalized Riesz Transforms on Orlicz-Hardy Spaces Associated to Operators
Relations among Besov-type spaces, Triebel-Lizorkin-type spaces and generalized Carleson measure spa
The Hardy space H-1 on non-homogeneous metric spaces
Weighted norm inequalities for multilinear Calderón-Zygmund operators on non-homogeneous metric meas
Multilinear analysis on metric spaces
Littlewood–Paley characterization and duality of weighted anisotropic product Hardy spaces
Hausdorff Besov-type and Triebel–Lizorkin-type spaces and their applications
The molecular characterization of the Hardy space on non-homogeneous metric measure spaces and its a
Boundedness of second order Riesz transforms associated to Schr？dinger operators on Musielak-Orlicz-
Embedding properties of Besov-type spaces
The radial lemma of strauss in the context of morrey spaces
Interpolation of morrey spaces on metric measure spaces
Morrey-type spaces on gauss measure spaces and boundedness of singular integrals
Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions
POINTWISE MULTIPLIERS FOR CAMPANATO SPACES ON GAUSS MEASURE SPACES
Musielak-Orlicz Besov-type and Triebel-Lizorkin-type spaces
GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES
Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces
Boundedness of fractional integrals on weighted Orlicz-Hardy spaces
Boundedness of maximal Calderón-Zygmund operators on non-homogeneous metric measure spaces
L∞-variational problems associated to measurable Finsler structures
Besov-type spaces with variable smoothness and integrability
Regularity and capacity for the fractional dissipative operator
Hardy spaces associated with a pair of commuting operators
Non-tangential maximal function characterizations of Hardy spaces associated with degenerate ellipti
Interpolation of Morrey-Campanato and related smoothness spaces.
Weak Hardy spaces WHpL(Rn) associated to operators satisfying k-Davies-Gaffney estimates
Littlewood-Paley characterizations of anisotropic Hardy spaces of Musielak-Orlicz type
Hardy spaces Hp over non-homogeneous metric measure spaces and their applications
Anisotropic Hardy spaces of Musielak-Orlicz type with applications to boundedness of sublinear opera
The molecular characterization of the Hardy space H-1 on non-homogeneous metric measure spaces and i
Musielak-Orlicz-Hardy spaces associated with operators satisfying reinforced off-diagonal estimates
New Characterizations of Besov-Triebel-Lizorkin-Hausdorff Spaces Including Coorbits and Wavelets
A NEW CHARACTERIZATION OF TRIEBEL-LIZORKIN SPACES ON Rn
Triebel-Lizorkin type spaces with variable exponents
Second-order Riesz transforms and maximal inequalities associated with magnetic Schr？dinger operator
Intrinsic square function characterizations of Musielak-Orlicz Hardy spaces
Characterizations of Besov and Triebel-Lizorkin spaces via averages on balls
Embedding properties of weighted Besov-type spaces
Newton-Besov spaces and Newton-Triebel-Lizorkin spaces on metric measure spaces
Fractional Haj？asz-Morrey-Sobolev spaces on quasi-metric measure spaces
Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated with magnetic Schr？din
Boundedness of Calderon-Zygmund operators with finite non-doubling measures
著作
The Hardy Space H1 with Non-doubling Measures and Their Applications
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