Extrapolation to Herz spaces with variable exponents and applications

2019 ◽  
Vol 33 (2) ◽  
pp. 437-463
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Variable Exponents ◽  
Herz Spaces

scholarly journals Commutators of the Bilinear Hardy Operator on Herz Type Spaces with Variable Exponents

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Shengrong Wang ◽  
Jingshi Xu
Keyword(s):  
Morrey Spaces ◽  
Hardy Operator ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Bmo Functions ◽  
Type Spaces

In this paper, we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of Herz spaces and Herz-Morrey spaces with variable exponents.

scholarly journals θ-type Calderón-Zygmund Operators and Commutators in Variable Exponents Herz space

2018 ◽  
Vol 16 (1) ◽  
pp. 1607-1620
Author(s):  
Yanqi Yang ◽  
Shuangping Tao
Keyword(s):  
Lipschitz Function ◽  
Herz Space ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Bmo Function

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.

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