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arXiv · 1203.4337

Necessary and sufficient conditions for boundedness of commutators of the general fractional integral operators on weighted Morrey spaces

Zengyan Si·Fayou Zhao
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Abstract

We prove that $b$ is in $Lip_{\bz}(\bz)$ if and only if the commutator $[b,L^{-α/2}]$ of the multiplication operator by $b$ and the general fractional integral operator $L^{-α/2}$ is bounded from the weighed Morrey space $L^{p,k}(ω)$ to $L^{q,kq/p}(ω^{1-(1-α/n)q},ω)$, where $0<β<1$, $0<α+β \frac{1-k}{p/q-k},$ and here $r_ω$ denotes the critical index of $ω$ for the reverse Hölder condition.

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Zengyan Si, Fayou Zhao. 2012-03-20. Necessary and sufficient conditions for boundedness of commutators of the general fractional integral operators on weighted Morrey spaces. https://arxiv.org/abs/1203.4337

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