Multilinear commutators of vector-valued intrinsic square functions on vector-valued generalized weighted Morrey spaces

Vagif S Guliyev,Mn Omarova

doi:10.1186/1029-242x-2014-258

Abstract

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogs of intrinsic square functions in the generalized weighted Morrey spaces M w p , φ ( l 2 ). We study the boundedness of intrinsic square functions including the Lusin area integral, the Littlewood-Paley g-function and g λ ∗ -function, and their multilinear commutators on vector-valued generalized weighted Morrey spaces M w p , φ ( l 2 ). In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on φ(x,r) without assuming any monotonicity property of φ(x,r) on r.MSC:42B25, 42B35.

Highlights

It is well known that the commutator is an important integral operator and it plays a key role in harmonic analysis
The commutator of Calderón-Zygmund operators plays an important role in studying the regularity of solutions of elliptic partial differential equations of second order
The classical Morrey spaces were originally introduced by Morrey in [ ] to study the local behavior of solutions to second order elliptic partial differential equations

Summary

Introduction

It is well known that the commutator is an important integral operator and it plays a key role in harmonic analysis. The commutator of Calderón-Zygmund operators plays an important role in studying the regularity of solutions of elliptic partial differential equations of second order (see, for example, [ – ]). The intrinsic square functions were first introduced by Wilson in [ , ] . .) be a sequence of locally integrable functions on Rn. For any x ∈ Rn, Wilson [ ] defined the vector-valued intrinsic square functions of f by Gαf (x) l and proved the following result. Liu [ ] studied the boundedness of intrinsic square functions on weighted Hardy spaces. In [ ], Wang considered intrinsic functions and the commutators generated with BMO functions on weighted Morrey spaces.

Theorem B

Then for λ

For p

Gα f

Findings

Since λ