Parametric Marcinkiewicz integrals on weighted Herz Spaces

Abstract

Abstract. Let 0 < < n and ˝b e the parametric Marcinkiewicz integral. In this paper we shall obtain the strong type and weak type estimates of ˝o n the weighted Herz spaces P K˛; p q .! 1 ; ! 2 / with general weights. The boundedness of the commutators generated by BMO functions and parametric Marcinkiewicz integral is also obtained.