Summability of Fourier series in periodic Hardy spaces with variable exponent

2020 ◽  
Vol 162 (2) ◽  
pp. 557-583
Author(s):  
F. Weisz
Keyword(s):  
Fourier Series ◽  
Hardy Spaces ◽  
Variable Exponent ◽  
Summability Of Fourier Series

Wiener amalgams, Hardy spaces and summability of Fourier series

2008 ◽  
Vol 145 (2) ◽  
pp. 419-442 ◽  
Author(s):  
FERENC WEISZ
Keyword(s):  
Fourier Series ◽  
Hardy Spaces ◽  
Summability Method ◽  
Wiener Amalgam Spaces ◽  
Almost Everywhere ◽  
Convergence Results ◽  
Special Cases ◽  
Summability Of Fourier Series ◽  
Amalgam Spaces ◽  
General Summability

AbstractA general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebraW(C,ℓ1)($\mathbb{R}$d). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from theHpHardy space toLp(orHp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

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

GENERALIZED MEANS AND THE SUMMABILITY OF FOURIER SERIES

1931 ◽  
Vol os-2 (1) ◽  
pp. 207-229 ◽  
Author(s):  
L. S. BOSANQUET ◽  
E. H. LINFOOT
Keyword(s):  
Fourier Series ◽  
Summability Of Fourier Series
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