θ-type Calderón-Zygmund Operators and Commutators in Variable Exponents Herz space
The 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 K˙p(⋅)...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-12-01
|
| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2018-0133 |
| Summary: | The 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 K˙p(⋅)α,q(⋅)(Rn).$\begin{array}{}
\displaystyle
\dot{K}^{\alpha,q(\cdot)}_{p(\cdot)}(\mathbb{R}^{n}).
\end{array}$ Furthermore, the boundedness of the corresponding commutators generated by BMO function and Lipschitz function is also obtained respectively. |
|---|---|
| ISSN: | 2391-5455 |