BOUNDEDNESS OF LITTLEWOOD-PALEY OPERATORS WITH VARIABLE KERNEL ON THE WEIGHTED HERZ-MORREY SPACES WITH VARIABLE EXPONENT

Abstract

Let Ω∈L∞(ℝn)×L2(Sn-1) be a homogeneous function of degree zero. In this article, we obtain some boundedness of the parameterized Littlewood-Paley operators with variable kernels on weighted Herz-Morrey spaces with variable exponent. As a supplement, the boundedness of fractional integral operators with variable kernel is also obtained on these spaces.

Keywords

• parameterized littlewood-paley operators
• variable kernel
• weighted herz space
• muckenhoupt weight. variable exponent