Collectanea Mathematica ( IF 0.7 ) Pub Date : 2020-12-11 , DOI: 10.1007/s13348-020-00309-y Bin Liu , Jouni Rättyä
Compact differences of two weighted composition operators acting from the weighted Bergman space \(A^p_{\omega }\) to another weighted Bergman space \(A^q_{\nu }\), where \(0<p\le q<\infty \) and \(\omega ,\nu \) belong to the class \({\mathcal {D}}\) of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proof a new description of q-Carleson measures for \(A^p_{\omega }\), with \(\omega \in {\mathcal {D}}\), in terms of pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space \(A^p_{\alpha }\) with \(-1<\alpha <\infty \) to the setting of doubling weights.
中文翻译:
加权合成算子的紧凑差异
从加权Bergman空间\(A ^ p _ {\ omega} \到另一个加权Bergman空间\(A ^ q _ {\ nu} \)作用的两个加权合成算子的紧致差分,其中\(0 <p \ le q表征<\ infty \)和\(\ omega,\ nu \)属于满足双向加倍条件的径向权重的类({\ mathcal {D}} \)。在证明的路上,用伪双曲圆盘用\(\ omega \ in {\ mathcal {D}} \)对\(A ^ p _ {\ omega} \)的q -Carleson度量的新描述是成立。最后提到的结果概括了q的众所周知的特征-Carleson将经典加权Bergman空间\(A ^ p _ {\ alpha} \)与\(-1 <\ alpha <\ infty \)设置为加倍权重。