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基于几类算子的函数空间实变理论
  • 项目名称：基于几类算子的函数空间实变理论
  • 项目类别：面上项目
  • 批准号：10871025
  • 申请代码：A010504
  • 项目来源：国家自然科学基金
  • 研究期限：2009-01-01-2011-12-31
  • 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：2008
中文摘要：

数学和物理中的许多分析问题均可归结为研究算子的各种性质，而刻画算子的这些性质离不开相应函数空间的实变理论.本课题系统地发展了一套欧式空间上Besov-Triebel-Lizorkin型空间理论,建立了Besov-Triebel-Lizorkin空间的点态特征刻画并获得了拟共形映照在某些Triebel-Lizorkin空间上的不变性; 建立了RD-空间的几个等价特征刻画并得到了其上原子Hardy空间的径向极大函数特征；在欧氏空间、Lipschitz区域和RD-空间上建立了与可允许函数及算子(包括热半群核满足Poisson上界估计的算子、二阶散度型椭圆算子、Schr?dinger型算子等)相关的(局部)(Orlicz-)Hardy空间理论及其对偶和前对偶空间理论,并应用于Riesz变换和Littlewood-Paley函数等算子有界性的研究中; 基于Gauss测度引进了局部倍测度空间并构造了其上的恒等逼近,同时构造了ax+b群上的二进结构,并应用于Hardy空间等函数空间及谱乘子等奇异积分算子有界性的研究中.这些结果为研究调和分析与偏微分方程等学科中的相关分析问题提供了新的工作空间和方法.

中文主题词： 欧式空间及其区域；齐型空间；非齐型空间；函数空间；算子
结论摘要：

英文主题词Euclidean space and its domian; homogeneous space; non-homogeneous space; function space; operator

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
  • 65
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期刊论文
Boundedness of paraproduct operators on RD-spaces
Estimates for Lusin-area and Littlewood-Paley g(lambda)* functions over spaces of homogeneous type
Weighted anisotropic product Hardy spaces and boundedness of sublinear operators
CHARACTERIZATIONS OF BMO ASSOCIATED WITH GAUSS MEASURES VIA COMMUTATORS OF LOCAL FRACTIONAL INTEGRAL
BOUNDEDNESS OF GENERALIZED RIESZ POTENTIALS ON SPACES OF HOMOGENEOUS TYPE
Radial maximal function characterizations of Hardy spaces on RD-spaces and their applications
An off-diagonal Marcinkiewicz interpolation theorem on Lorentz spaces
REAL-VARIABLE CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BESSEL OPERATORS
Pointwise characterizations of Besov and Triebel-Lizorkin spaces and quasiconformal mappings
LOCALIZED HARDY SPACES H(1) RELATED TO ADMISSIBLE FUNCTIONS ON RD-SPACES AND APPLICATIONS TO SCHRODI
Equivalent Characterizations for Boundedness of Maximal Singular Integrals on ax plus b-Groups
Boundedness of Lusin-area and g(lambda)* functions on localized BMO spaces over doubling metric meas
Multiple-weighted norm inequalities for maximal multi-linear singular integrals with non-smooth kern
Applications of Orlicz-Hardy spaces associated with operators satisfying Poisson estimates
Boundedness of Lusin-area and g(lambda)* functions on localized Morrey-Campanato spaces over doublin
Predual Spaces of Banach Completions of Orlicz-Hardy Spaces Associated with Operators
Maximal function characterizations of Hardy spaces associated with Schrodinger operators on nilpoten
NEW CHARACTERIZATIONS OF WEIGHTED MORREY-CAMPANATO SPACES
REAL INTERPOLATION FOR GRAND BESOV AND TRIEBEL-LIZORKIN SPACES ON RD-SPACES
Elementary characterizations of generalized weighted Morrey-Campanato spaces
New applications of Besov-type and Triebel-Lizorkin-type spaces
A characterization of Hajlasz-Sobolev and Triebel-Lizorkin spaces via grand Littlewood-Paley functio
HARDY SPACES H(L)(1) (R(n)) ASSOCIATED TO SCHRODINGER TYPE OPERATORS (-Delta)(2) + V(2)
Characterizations of Besov-type and Triebel-Lizorkin-type spaces via maximal functions and local mea
Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications
Anisotropic singular integrals in product spaces
Characterizations of localized BMO(R-n) via commutators of localized Riesz transforms and fractional
A JORDAN SOBOLEV EXTENSION DOMAIN
Boundedness of Littlewood-Paley Operators Associated with Gauss Measures
Boundedness of sublinear operators on product Hardy spaces and its application
New Orlicz-Hardy spaces associated with divergence form elliptic operators
LOCALIZED BMO AND BLO SPACES ON RD-SPACES AND APPLICATIONS TO SCHRODINGER OPERATORS
Generalized Vanishing Mean Oscillation Spaces Associated with Divergence Form Elliptic Operators
LOCALIZED MORREY-CAMPANATO SPACES ON METRIC MEASURE SPACES AND APPLICATIONS TO SCHRODINGER OPERATORS
Boundedness of Calderon-Zygmund operators on non-homogeneous metric measure spaces: equivalent chara
Boundedness of Caldern-Zygmund operators in product Hardy spaces
Localized Hardy spaces associated with operators
Atomic hardy-type spaces between H (1) and L (1) on metric spaces with non-doubling measures
DISSERTATIONES MATHEMATICAE
Boundedness of linear operators via atoms on Hardy spaces with non-doubling measures
Spaces of type BLO on non-homogeneous metric measure
New properties of Besov and Triebel-Lizorkin spaces on RD-spaces
ORLICZ-HARDY SPACES ASSOCIATED WITH OPERATORS SATISFYING DAVIES-GAFFNEY ESTIMATES
Dual Properties of Triebel-Lizorkin-Type Spaces and their Applications
Boundedness of Calderón-Zygmund operators in product Hardy spaces
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