scholarly journals Wavelet characterization of local Muckenhoupt weighted Lebesgue spaces with variable exponent

2020 ◽  
Vol 198 ◽  
pp. 111930
Author(s):  
Mitsuo Izuki ◽  
Toru Nogayama ◽  
Takahiro Noi ◽  
Yoshihiro Sawano
Keyword(s):  
Variable Exponent ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces

The one-sided Ap conditions and local maximal operator

2011 ◽  
Vol 55 (1) ◽  
pp. 79-104 ◽  
Author(s):  
Ana L. Bernardis ◽  
Amiran Gogatishvili ◽  
Francisco Javier Martín-Reyes ◽  
Pedro Ortega Salvador ◽  
Luboš Pick
Keyword(s):  
Function Space ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Banach Function Space ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
The One

AbstractWe introduce the one-sided local maximal operator and study its connection to the one-sided Ap conditions. We get a new characterization of the boundedness of the one-sided maximal operator on a quasi-Banach function space. We obtain applications to weighted Lebesgue spaces and variable-exponent Lebesgue spaces.

The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
Humberto Rafeiro ◽  
Makhmadiyor Yakhshiboev
Keyword(s):  
Integral Operator ◽  
Fractional Derivative ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Inverse Operator ◽  
Fractional Integral Operator ◽  
Left Inverse ◽  
Fractional Differentiation ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces

AbstractAfter recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.

Characterization of a Two-Weighted Vector-Valued Inequality for Fractional Maximal Operators

1998 ◽  
Vol 5 (6) ◽  
pp. 583-600
Author(s):  
Y. Rakotondratsimba
Keyword(s):  
Maximal Operator ◽  
Maximal Operators ◽  
Lebesgue Spaces ◽  
Fractional Maximal Operator ◽  
Weighted Lebesgue Spaces ◽  
Vector Valued

Abstract We give a characterization of the weights 𝑢(·) and 𝑣(·) for which the fractional maximal operator 𝑀𝑠 is bounded from the weighted Lebesgue spaces 𝐿𝑝(𝑙𝑟, 𝑣𝑑𝑥) into 𝐿𝑞(𝑙𝑟, 𝑢𝑑𝑥) whenever 0 ≤ 𝑠 < 𝑛, 1 < 𝑝, 𝑟 < ∞, and 1 ≤ 𝑞 < ∞.

scholarly journals Approximation theorems in weighted Lebesgue spaces with variable exponent

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 561-577
Author(s):  
Ahmet Testici
Keyword(s):  
Weight Function ◽  
Approximation Theory ◽  
Variable Exponent ◽  
Approximation Properties ◽  
Lebesgue Spaces ◽  
Approximation Theorems ◽  
Weighted Lebesgue Spaces ◽  
Muckenhoupt Class

In this work, approximation properties of de la Vall?e-Poussin means are investigated in weighted Lebesgue spaces with variable exponent where weight function belongs to Muckenhoupt class. For this purpose direct, inverse and simultaneous theorems of approximation theory are proved and constructive characterizations of functions are obtained in weighted Lebesgue spaces with variable exponent.

scholarly journals A revisit on the compactness of commutators

2020 ◽  
pp. 1-31
Author(s):  
Weichao Guo ◽  
Huoxiong Wu ◽  
Dongyong Yang
Keyword(s):  
Lebesgue Spaces ◽  
First Order ◽  
Weighted Lebesgue Spaces ◽  
Local Mean

Abstract A new characterization of $\text {CMO}(\mathbb R^n)$ is established replying upon local mean oscillations. Some characterizations of iterated compact commutators on weighted Lebesgue spaces are given, which are new even in the unweighted setting for the first order commutators.

scholarly journals Boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and Morrey-Herz spaces with variable exponents

2021 ◽  
Vol 6 (10) ◽  
pp. 11246-11262
Author(s):  
Yueping Zhu ◽  
◽  
Yan Tang ◽  
Lixin Jiang ◽  
Keyword(s):  
Variable Exponent ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Lebesgue Spaces ◽  
Singular Operators ◽  
Weighted Lebesgue Spaces

<abstract><p>In this paper, we introduce weighted Morrey-Herz spaces $ M\dot K^{\alpha, \lambda}_{q, p(\cdot)}(w~^{p(\cdot)}) $ with variable exponent $ p(\cdot) $. Then we prove the boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and weighted Morrey-Herz spaces with variable exponents.</p></abstract>

Sign in / Sign up

Export Citation Format

Share Document