Potential Analysis ( IF 1.0 ) Pub Date : 2020-01-11 , DOI: 10.1007/s11118-019-09814-7 Jin Tao , Dachun Yang , Dongyong Yang
Let \(p\in (1, \infty )\), ? ? (0,1) and \(w\in A_{p}({\mathbb C}).\) In this article, the authors obtain a boundedness (resp., compactness) characterization of the Beurling–Ahlfors commutator \([\mathcal B, b]\) on the weighted Morrey space \(L_{w}^{p, \kappa }(\mathbb C)\) via \(\text {BMO}({\mathbb C})\) [resp., \(\text {CMO}({\mathbb C})\)], where \(\mathcal B\) denotes the Beurling–Ahlfors transform and \(b\in \text {BMO}({\mathbb C})\) [resp., \(\text {CMO}({\mathbb C})\)]. Moreover, an application to the Beltrami equation is also given.
中文翻译:
加权Morrey空间上的Beurling–Ahlfors交换子及其在Beltrami方程中的应用
让\(P \(1,\ infty)\) ,? ?(0,1)和\(w_in A_ {p}({\ mathbb C})。\)在本文中,作者获得了Beurling–Ahlfors换向器\([通过\(\ text {BMO}({\ mathbb C})\)在加权Morrey空间\(L_ {w} ^ {p,\ kappa}(\ mathbb C)\)上的\ mathcal B,b] \) [resp。,\(\ text {CMO}({\ mathbb C})\) ],其中\(\ mathcal B \)表示Beurling-Ahlfors变换和\(b \ in \ text {BMO}({\ mathbb C})\) [resp。,\(\ text {CMO}({\ mathbb C})\) ]。此外,还给出了对Beltrami方程的应用。