herz space
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2021 ◽  
Vol 33 (5) ◽  
pp. 1097-1123
Author(s):  
Mingquan Wei

Abstract This paper extends the extrapolation theory to product Herz spaces. To prove the main result, we first investigate the dual space of the product Herz space, and then show the boundedness of the strong maximal operator on product Herz spaces. By using this extrapolation theory, we establish the John–Nirenberg inequality, the characterization of little bmo, the Fefferman–Stein vector-valued inequality, the boundedness of the bi-parameter singular integral operator, the strong fractional maximal operator, and the bi-parameter fractional integral operator on product Herz spaces. We also give a new characterization of little bmo via the boundedness of the commutators of some bi-parameter operators on product Herz spaces. Even in the one-parameter setting, some of our results are new.



2019 ◽  
Vol 11 (2) ◽  
pp. 753-787 ◽  
Author(s):  
Nguyen Minh Chuong ◽  
Dao Van Duong ◽  
Nguyen Duc Duyet


2018 ◽  
Vol 16 (1) ◽  
pp. 1607-1620
Author(s):  
Yanqi Yang ◽  
Shuangping Tao

AbstractThe aim of this paper is to deal with the boundedness of the θ-type Calderón-Zygmund operators and their commutators on Herz spaces with two variable exponents p(⋅), q(⋅). It is proved that the θ-type Calderón-Zygmund operators are bounded on the homogeneous Herz space with variable exponents $\begin{array}{} \displaystyle \dot{K}^{\alpha,q(\cdot)}_{p(\cdot)}(\mathbb{R}^{n}). \end{array}$ Furthermore, the boundedness of the corresponding commutators generated by BMO function and Lipschitz function is also obtained respectively.







2017 ◽  
Vol 11 (3) ◽  
pp. 513-535 ◽  
Author(s):  
Jianmiao Ruan ◽  
Dashan Fan ◽  
Qingyan Wu


2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Hongbin Wang ◽  
Jiajia Wang ◽  
Zunwei Fu

We define the new central Morrey space with variable exponent and investigate its relation to the Morrey-Herz spaces with variable exponent. As applications, we obtain the boundedness of the homogeneous fractional integral operator TΩ,σ and its commutator [b,TΩ,σ] on Morrey-Herz space with variable exponent, where Ω∈Ls(Sn-1) for s≥1 is a homogeneous function of degree zero, 0<σ<n, and b is a BMO function.



2016 ◽  
Vol 15 (01) ◽  
pp. 107-121 ◽  
Author(s):  
Ferenc Weisz

In this paper, a general summability method of multi-dimensional Fourier transforms, the so-called [Formula: see text]-summability, is investigated. It is shown that if [Formula: see text] is in a Herz space, then the summability means [Formula: see text] of a function [Formula: see text] converge to [Formula: see text] at each modified Lebesgue point, whenever [Formula: see text] and [Formula: see text] is in a cone. The same holds for Fourier series. Some special cases of the [Formula: see text]-summation are considered, such as the Weierstrass, Abel, Picard, Bessel, Fejér, Cesàro, de la Vallée-Poussin, Rogosinski and Riesz summations.



2016 ◽  
Vol 8 (3) ◽  
pp. 204-216 ◽  
Author(s):  
N. M. Chuong ◽  
D. V. Duong
Keyword(s):  


2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Amjad Hussain ◽  
Guilian Gao

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.



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