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”,

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

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

scholarly journals The higher order commutators of the fractional integrals on Hardy spaces

2005 ◽  
Vol 79 (1) ◽  
pp. 11-24
Author(s):  
Shunchao Long ◽  
Jian Wang
Keyword(s):  
Hardy Spaces ◽  
Fractional Integral ◽  
Higher Order ◽  
Type Operator ◽  
Fractional Integrals ◽  
Integral Type ◽  
Bmo Function

AbstractIn this paper we investigate the boundedness on Hardy spaces for the higher order commutator Tb, m generated by the BMO function b and fractional integral type operator Tτ, and establish the boundness theorems for Tτb, m from Hp1.q1.sb, m to Lp2 and to Hp2 (0 < p1 ≤ 1), and from H Ka. p1.sq1, b, m to Ka.p2q2 and to H Ka. p2q2, respectively, for certain ranges of α, p1, q1, p2, q2 and s.

scholarly journals The boundedness of multilinear commutators on locally compact Vilenkin groups

2006 ◽  
Vol 4 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Canqin Tang
Keyword(s):  
Integral Operator ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Vilenkin Group ◽  
Lebesgue Spaces ◽  
Locally Compact ◽  
Vilenkin Groups ◽  
Multilinear Commutators

LetGbe a locally compact Vilenkin group. In this paper, the authors investigate the boundedness of multilinear commutators of fractional integral operator on Lebesgue spaces onG. Furthermore, the boundedness on Hardy spaces are also obtained in this paper.

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
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