Hardy Spaces Associated to Critical Herz Spaces with Variable Exponent

2016 ◽  
Vol 13 (5) ◽  
pp. 2981-3013 ◽  
Author(s):  
Mitsuo Izuki ◽  
Takahiro Noi
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Herz Spaces

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 Characterizations of variable exponent Hardy spaces via Riesz transforms

2016 ◽  
Vol 29 (2) ◽  
pp. 245-270 ◽  
Author(s):  
Dachun Yang ◽  
Ciqiang Zhuo ◽  
Eiichi Nakai
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Riesz Transforms

scholarly journals Variable Exponent Spaces of Analytic Functions

2020 ◽  
Author(s):  
Gerardo A. Chacón ◽  
Gerardo R. Chacón
Keyword(s):  
Hardy Spaces ◽  
Measurable Function ◽  
Analytic Functions ◽  
Variable Exponent ◽  
Bergman Spaces ◽  
Lebesgue Spaces ◽  
Basic Properties ◽  
Variable Exponent Spaces ◽  
Real Functions ◽  
Spaces Of Analytic Functions

Variable exponent spaces are a generalization of Lebesgue spaces in which the exponent is a measurable function. Most of the research done in this topic has been situated under the context of real functions. In this work, we present two examples of variable exponent spaces of analytic functions: variable exponent Hardy spaces and variable exponent Bergman spaces. We will introduce the spaces together with some basic properties and the main techniques used in the context. We will show that in both cases, the boundedness of the evaluation functionals plays a key role in the theory. We also present a section of possible directions of research in this topic.

scholarly journals Strongly Singular Convolution Operators on Herz-Type Hardy Spaces with Variable Exponent

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Hongbin Wang ◽  
Dunyan Yan
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Convolution Operators

We investigate the boundedness of the strongly singular convolution operators on Herz-type Hardy spaces with variable exponent.

scholarly journals Multilinear Singular Integrals and Commutators on Herz Space with Variable Exponent

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Amjad Hussain ◽  
Guilian Gao
Keyword(s):  
Singular Integral ◽  
Variable Exponent ◽  
Singular Integrals ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Herz Space ◽  
Herz Spaces ◽  
Multilinear Singular Integrals

The paper establishes some sufficient conditions for the boundedness of singular integral operators and their commutators from products of variable exponent Herz spaces to variable exponent Herz spaces.

scholarly journals Endpoint Estimates for Fractional Hardy Operators and Their Commutators on Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jiang Zhou ◽  
Dinghuai Wang
Keyword(s):  
Hardy Spaces ◽  
Herz Spaces ◽  
Multilinear Commutators ◽  
Hardy Operators

(Hpℝn,Lqℝn)bounds of fractional Hardy operators are obtained. Moreover, the estimates for commutators of fractional Hardy operators on Hardy spaces are worked out. It is also proved that the commutators of fractional Hardy operators are mapped from the Herz-type Hardy spaces into the Herz spaces. The estimates for multilinear commutators of fractional Hardy operators are also discussed.

scholarly journals Higer-order commutators of parametrized Marcinkewicz integrals on Herz spaces with variable exponent

2020 ◽  
Vol 3 (1) ◽  
pp. 56-70
Author(s):  
Omer Abdalrhman ◽  
◽  
Afif Abdalmonem ◽  
Shuangping Tao ◽  
◽  
...  
Keyword(s):  
Variable Exponent ◽  
Herz Spaces
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