Abstract Hardy spaces with variable exponents

2018 ◽  
Vol 167 ◽  
pp. 29-50 ◽  
Author(s):  
Yin Liu ◽  
Jiman Zhao
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents

scholarly journals Variable Anisotropic Hardy Spaces with Variable Exponents

2021 ◽  
Vol 9 (1) ◽  
pp. 65-89
Author(s):  
Zhenzhen Yang ◽  
Yajuan Yang ◽  
Jiawei Sun ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Moment Condition ◽  
Variable Exponents ◽  
Hölder Continuous ◽  
Multi Level ◽  
The Moment ◽  
Variable Anisotropy

Abstract Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

scholarly journals Hardy spaces with variable exponents and generalized Campanato spaces

2012 ◽  
Vol 262 (9) ◽  
pp. 3665-3748 ◽  
Author(s):  
Eiichi Nakai ◽  
Yoshihiro Sawano
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents

scholarly journals Local Hardy Spaces with Variable Exponents Associated with Non-negative Self-Adjoint Operators Satisfying Gaussian Estimates

2019 ◽  
Vol 30 (3) ◽  
pp. 3275-3330 ◽  
Author(s):  
Víctor Almeida ◽  
Jorge J. Betancor ◽  
Estefanía Dalmasso ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents ◽  
Local Hardy Spaces ◽  
Adjoint Operators ◽  
Gaussian Estimates

Fractional Integral on Martingale Hardy Spaces With Variable Exponents

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Zhiwei Hao ◽  
Yong Jiao
Keyword(s):  
Hardy Spaces ◽  
Probability Space ◽  
Fractional Integral ◽  
Integral Operators ◽  
Variable Exponents ◽  
Fractional Integral Operators

AbstractIn this paper we investigate the boundedness of fractional integral operators on predictable martingale Hardy spaces with variable exponents defined on a probability space. More precisely, let f = (f

Corrigendum: Fractional integral on martingale hardy spaces with variable exponents

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Yong Jiao ◽  
Dejian Zhou ◽  
Ferenc Weisz ◽  
Zhiwei Hao
Keyword(s):  
Hardy Spaces ◽  
Fractional Integral ◽  
Variable Exponents

AbstractThis is an erratum to the paper “Fractional integral on martingale Hardy spaces with variable exponents”,

scholarly journals Molecular Decomposition of Anisotropic Hardy Spaces With Variable Exponents

2020 ◽  
Vol 51 (4) ◽  
pp. 1471-1495
Author(s):  
Wenhua Wang ◽  
Xiong Liu ◽  
Aiting Wang ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents ◽  
Molecular Decomposition

Sublinear operators on weighted Hardy spaces with variable exponents

2019 ◽  
Vol 31 (3) ◽  
pp. 607-617 ◽  
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents ◽  
Square Functions ◽  
Weighted Hardy Spaces ◽  
Riesz Means ◽  
Marcinkiewicz Integrals ◽  
Sublinear Operators ◽  
Intrinsic Square Functions

Abstract We establish the mapping properties for some sublinear operators on weighted Hardy spaces with variable exponents by using extrapolation. In particular, we study the Calderón–Zygmund operators, the maximal Bochner–Riesz means, the intrinsic square functions and the Marcinkiewicz integrals on weighted Hardy spaces with variable exponents.

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.

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