Inequality estimates for the boundedness of multilinear singular and fractional integral operators

Xiaosha Zhou,Chuangxia Huang,Haijun Hu,Li Liu

doi:10.1186/1029-242x-2013-303

Abstract

Abstract In this paper, the inequality of boundedness for the multilinear fractional singular integral operators associated to the weighted Lipschitz functions is estimated. The operators include the Calderón-Zygmund singular integral operator and the fractional integral operator. MSC:42B20, 42B25.

Highlights

As the development of the singular integral operators, their commutators and multilinear operators have been well studied
In [, – ], the authors proved that the commutators and multilinear operators generated by the singular integral operators and BMO functions are bounded on Lp(Rn) for < p < ∞
In [ – ], the boundedness for the commutators and multilinear operators generated by the singular integral operators and Lipschitz functions on Lp(Rn) ( < p < ∞) and TriebelLizorkin spaces are obtained

Summary

Introduction

As the development of the singular integral operators, their commutators and multilinear operators have been well studied (see [ – ]). In [ – , – ], the authors proved that the commutators and multilinear operators generated by the singular integral operators and BMO functions are bounded on Lp(Rn) for < p < ∞. In [ – ], the boundedness for the commutators and multilinear operators generated by the singular integral operators and Lipschitz functions on Lp(Rn) ( < p < ∞) and TriebelLizorkin spaces are obtained.

Objectives

Results

Conclusion