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

Abstract

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.

Keywords

• θ-type calderón-zygmund operator
• commutator
• herz spaces with variable exponent
• bmo space
• 42b20
• 42b25
• 42b35