A two‐weight estimate for a class of fractional integral operators with rough kernel

Yong Ding

doi:10.1155/ijmms.2005.1835

Abstract

We prove that the operators in a class of rough fractional integral operators and the related maximal operators are bounded from Lp(vp) to Lq(uq) with weight pair (u, v).

Highlights

Introduction and resultsSuppose that Ω ∈ Ls(Sn−1) (s ≥ 1) is homogeneous of degree zero in Rn with zero mean value on Sn−1, it is well known that the Calderon-Zygmund singular integral is defined byΩ(x − y) TΩ f (x) = p.v
We prove that the operators in a class of rough fractional integral operators and the related maximal operators are bounded from Lp(vp) to Lq(uq) with weight pair (u, v)
In 1967, Bajsanski and Coifman [1] first discussed the boundedness of operators on a class of singular integral operators TΩA which are associated with the commutators of the Calderon-Zygmund singular integral TΩ

Summary

Introduction

We prove that the operators in a class of rough fractional integral operators and the related maximal operators are bounded from Lp(vp) to Lq(uq) with weight pair (u, v). 1836 Two-weight estimate for fractional integral operators for 0 < α < n. In a very simple way, which is altogether different from the method in [3, 4], we will obtain the weighted (Lp, Lq) boundedness with the weight pair (u, v) for the rough fractional integral operator TΩA,α, which is defined by TΩA,α f (x) =

Results

Conclusion