Singular integrals and sublinear operators on amalgam spaces and Hardy-amalgam spaces

2021 ◽  
Vol 127 (3) ◽  
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Singular Integrals ◽  
Square Function ◽  
Sublinear Operators ◽  
Intrinsic Square Function ◽  
Amalgam Spaces ◽  
Extrapolation Theory

In this paper, we establish the extrapolation theory for the amalgam spaces and the Hardy-amalgam spaces. By using the extrapolation theory, we obtain the mapping properties for the Calderón-Zygmund operators and its commutator, the Carleson operators and establish the Rubio de Francia inequalities for Littlewood-Paley functions of arbitrary intervals to the amalgam spaces. We also obtain the boundedness of the Calder{ó}n-Zygmund operators and the intrinsic square function on the Hardy-amalgam spaces.

scholarly journals Norm variation of ergodic averages with respect to two commuting transformations

2017 ◽  
Vol 39 (3) ◽  
pp. 658-688 ◽  
Author(s):  
POLONA DURCIK ◽  
VJEKOSLAV KOVAČ ◽  
KRISTINA ANA ŠKREB ◽  
CHRISTOPH THIELE
Keyword(s):  
Harmonic Analysis ◽  
Hilbert Transform ◽  
Singular Integrals ◽  
Quantitative Result ◽  
Square Function ◽  
Two Dimensional ◽  
Ergodic Averages ◽  
Multilinear Singular Integrals

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.

scholarly journals Two weight norm inequalities for communtators of one-sided singular integrals and the one-sided discrete square function

2005 ◽  
Vol 79 (1) ◽  
pp. 77-94 ◽  
Author(s):  
M. Lorente ◽  
M. S. Riveros
Keyword(s):  
Singular Integrals ◽  
Square Function ◽  
Strong Type ◽  
Norm Inequalities ◽  
The One

AbstractThe purpose of this paper is to prove strong type inequalities with pairs of related weights for commutators of one-sided singular integrals (given by a Calderón-Zygmund kernel with support in (-∞, 0)) and the one-sided discrete square function. The estimate given by C. Segovia and J. L. Torrea is improved for these one-sided operators giving a wider class of weights for which the inequality holds.

scholarly journals Intrinsic Square Function Characterizations of Variable Hardy–Lorentz Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Khedoudj Saibi
Keyword(s):  
Measurable Function ◽  
Lorentz Space ◽  
Hölder Continuity ◽  
Continuity Condition ◽  
Lorentz Spaces ◽  
Square Function ◽  
Holder Continuity ◽  
Area Function ◽  
Intrinsic Square Function ◽  
Lusin Area Function

The aim of this paper is to establish the intrinsic square function characterizations in terms of the intrinsic Littlewood–Paley g-function, the intrinsic Lusin area function, and the intrinsic gλ∗-function of the variable Hardy–Lorentz space Hp⋅,qℝn, for p⋅ being a measurable function on ℝn satisfying 0<p−≔ess infx∈ℝnpx≤ess supx∈ℝnpx≕p+<∞ and the globally log-Hölder continuity condition and q∈0,∞, via its atomic and Littlewood–Paley function characterizations.

scholarly journals Two weight estimates for a class of (p, q) type sublinear operators and their commutators

2019 ◽  
Vol 17 (1) ◽  
pp. 758-775 ◽  
Author(s):  
Hu Yunpeng ◽  
Zhou Jiang ◽  
Cao Yonghui
Keyword(s):  
Norm Inequalities ◽  
Type Space ◽  
Sublinear Operators ◽  
Amalgam Spaces

Abstract In the present paper, the authors investigate the two weight, weak-(p, q) type norm inequalities for a class of sublinear operators 𝓣γ and their commutators [b, 𝓣γ] on weighted Morrey and Amalgam spaces. What should be stressed is that we introduce the new BMO type space and our results generalize known results before.

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