Abstract
The purpose of this paper is to investigate the weighted estimates of commutators generated by BMO-functions and the fractional integral operator on Morrey spaces. The main result generalizes the Sawano, Sugano, and Tanaka result to a weighted setting.
Highlights
The aim of this paper is to investigate the weighted inequalities of commutators generated by BMO-functions and the fractional integral operator on Morrey spaces
The authors introduced the condition of weights in [ ]
Under a certain condition of the weights, we investigate the weighted estimates of commutators generated by BMO-functions and the fractional integral operator on Morrey spaces
Summary
The aim of this paper is to investigate the weighted inequalities of commutators generated by BMO-functions and the fractional integral operator on Morrey spaces. (Iαf )v Mqq ≤ C[v, w]aq ,r ,aq,p/a fw Mpp. In this paper, we investigate the boundedness of higher order commutators generated by BMO-functions and the fractional integral operator on Morrey spaces corresponding to Theorem E. For b ∈ BMO(Rn), we have [v, w]aq ,aq,p/a fw Corollary gives us the following inequality in letting p = p , q = q and v = w. |x – y|n–α f (y) dy and we may assume that the integral defining [b, I ,α](m)f (x) converges for a.e. x ∈ Rn. By a similar argument to the proof of Theorem , we have the following estimate.
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