scholarly journals The Molecular Characterization of Weighted Hardy Spaces

2002 ◽  
Vol 188 (2) ◽  
pp. 442-460 ◽  
Author(s):  
Ming-Yi Lee ◽  
Chin-Cheng Lin
Keyword(s):  
Molecular Characterization ◽  
Hardy Spaces ◽  
Weighted Hardy Spaces

The molecular characterization of weighted Hardy spaces

2001 ◽  
Vol 44 (2) ◽  
pp. 201-211 ◽  
Author(s):  
Xingmin Li ◽  
Lizhong Peng
Keyword(s):  
Molecular Characterization ◽  
Hardy Spaces ◽  
Weighted Hardy Spaces

Molecular characterization of anisotropic Musielak–Orlicz Hardy spaces and their applications

2016 ◽  
Vol 32 (11) ◽  
pp. 1391-1414 ◽  
Author(s):  
Bao De Li ◽  
Xing Ya Fan ◽  
Zun Wei Fu ◽  
Da Chun Yang
Keyword(s):  
Molecular Characterization ◽  
Hardy Spaces

Two-Weight Norm Inequality and Carleson Measure in Weighted Hardy Spaces

1992 ◽  
Vol 44 (6) ◽  
pp. 1206-1219 ◽  
Author(s):  
Dangsheng Gu
Keyword(s):  
Homogeneous Space ◽  
Hardy Spaces ◽  
Maximal Operator ◽  
Carleson Measure ◽  
Norm Inequality ◽  
Doubling Measure ◽  
Weight Norm Inequality ◽  
Weighted Hardy Spaces

AbstractLet (X, ν, d) be a homogeneous space and let Ω be a doubling measure on X. We study the characterization of measures μ on X+ = X x R+ such that the inequality , where q < p, holds for the maximal operator Hvf studied by Hörmander. The solution utilizes the concept of the “balayée” of the measure μ.

scholarly journals Fredholm Weighted Composition Operator on Weighted Hardy Space

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Liankuo Zhao
Keyword(s):  
Hardy Space ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Weighted Composition Operator ◽  
Weighted Hardy Space ◽  
Weighted Hardy Spaces ◽  
Weighted Composition

This paper gives a unified characterization of Fredholm weighted composition operator on a class of weighted Hardy spaces.

A new molecular characterization of diagonal anisotropic Musielak-Orlicz Hardy spaces

2021 ◽  
Vol 166 ◽  
pp. 102939
Author(s):  
Minfeng Liao ◽  
Jinxia Li ◽  
Bo Li ◽  
Baode Li
Keyword(s):  
Molecular Characterization ◽  
Hardy Spaces

scholarly journals The molecular characterization of anisotropic Herz-type Hardy spaces with two variable exponents

2020 ◽  
Vol 18 (1) ◽  
pp. 434-447
Author(s):  
Qingdong Guo ◽  
Wenhua Wang
Keyword(s):  
Hardy Space ◽  
Molecular Characterization ◽  
Hardy Spaces ◽  
Variable Exponents ◽  
Herz Type Hardy Space

Abstract In this article, the authors establish the characterizations of a class of anisotropic Herz-type Hardy spaces with two variable exponents associated with a non-isotropic dilation on {{\mathbb{R}}}^{n} in terms of molecular decompositions. Using the molecular decompositions, the authors obtain the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy space with two variable exponents.

LITTLEWOOD–PALEY CHARACTERIZATION OF WEIGHTED HARDY SPACES ASSOCIATED WITH OPERATORS

2016 ◽  
Vol 103 (2) ◽  
pp. 250-267 ◽  
Author(s):  
GUORONG HU
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Adjoint Operator ◽  
Weighted Hardy Space ◽  
Boundedness Condition ◽  
Weighted Hardy Spaces ◽  
Lusin Area Function ◽  
Extra Assumption ◽  
Type Decomposition

Let$(X,d,\unicode[STIX]{x1D707})$be a metric measure space endowed with a distance$d$and a nonnegative, Borel, doubling measure$\unicode[STIX]{x1D707}$. Let$L$be a nonnegative self-adjoint operator on$L^{2}(X)$. Assume that the (heat) kernel associated to the semigroup$e^{-tL}$satisfies a Gaussian upper bound. In this paper, we prove that for any$p\in (0,\infty )$and$w\in A_{\infty }$, the weighted Hardy space$H_{L,S,w}^{p}(X)$associated with$L$in terms of the Lusin (area) function and the weighted Hardy space$H_{L,G,w}^{p}(X)$associated with$L$in terms of the Littlewood–Paley function coincide and their norms are equivalent. This improves a recent result of Duonget al.[‘A Littlewood–Paley type decomposition and weighted Hardy spaces associated with operators’,J. Geom. Anal.26(2016), 1617–1646], who proved that$H_{L,S,w}^{p}(X)=H_{L,G,w}^{p}(X)$for$p\in (0,1]$and$w\in A_{\infty }$by imposing an extra assumption of a Moser-type boundedness condition on$L$. Our result is new even in the unweighted setting, that is, when$w\equiv 1$.

scholarly journals Molecular Characterization of Hardy Spaces Associated with Twisted Convolution

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jizheng Huang ◽  
Yu Liu
Keyword(s):  
Hardy Space ◽  
Molecular Characterization ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Twisted Convolution

We give a molecular characterization of the Hardy space associated with twisted convolution. As an application, we prove the boundedness of the local Riesz transform on the Hardy space.

scholarly journals Riesz Transform Characterization of Weighted Hardy Spaces Associated with Schrödinger Operators

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Hua Zhu
Keyword(s):  
Schrödinger Operator ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Nonnegative Function ◽  
Riesz Transforms ◽  
Schrodinger Operator ◽  
Weighted Hardy Spaces ◽  
Local Hardy Spaces ◽  
Reverse Hölder

We characterize the weighted local Hardy spaceshρ1(ω)related to the critical radius functionρand weightsω∈A1ρ,∞(Rn)by localized Riesz transformsR^j; in addition, we give a characterization of weighted Hardy spacesHL1(ω)via Riesz transforms associated with Schrödinger operatorL, whereL=-Δ+Vis a Schrödinger operator onRn(n≥3) andVis a nonnegative function satisfying the reverse Hölder inequality.

Sign in / Sign up

Export Citation Format

Share Document