Abstract:

The boundedness of the fractional type Marcinkiewicz integrals μΩ,α with variable kernels on Hardy spaces and Herz type Hardy spaces are established. Some properties of μΩ,α which kernel satisfies certain condition are given by the atomic decomposition theorem. Also, the integral μΩ,α is an operator of type H1,Lnn-α and of type (Hp,Lq). The boundedness from Herz type Hardy spaces to Herz spaces about the integral μΩ,α are presented.

Key words:  fractional Marcinkiewicz integral; variable kernels; Hardy spaces; Herz type Hardy spaces