We provide a characterization of the commutant analytic Toeplitz operators TB induced by finite Blaschke products B acting on weighted Bergman spaces which, as particular instance, yields case B(z)=zn space solved recently Abkar, Cao and Zhu [1]. Moreover, it extends previous results Cowen Wahl in this context applies to other Banach functions such Hardy Hp for 1<p<?. Finally, we apply approach...

The author has previously shown that a sequence in the unit disk is a zero sequence for the Bergman space A if and only if a certain weighted L space contains a non-zero (equivalently, zero-free) analytic function. The weight in question is given by a simple formula summed over the zero set. Here we show that a sequence in the unit disk is an interpolating sequence for A if and only if it is se...

We compute the exact value of essential norm a generalized Hilbert matrix operator acting on weighted Bergman spaces Avp and Banach Hv? analytic functions, where v is general radial weight. In particular, we obtain classical standard A?p for p>2+?,??0, Korenblum H?? 0<?<1. also cover Hardy space Hp,1<p<?, case. case, equal to conjectured its similarly in case coincide. Hw?? with weights w?(z)=(...