Toeplitz operators on Bergman spaces and Hardy multipliers
Tom 204 / 2011
Studia Mathematica 204 (2011), 137-154 MSC: Primary 47B35; Secondary 46E15. DOI: 10.4064/sm204-2-3
We study Toeplitz operators $T_a$ with radial symbols in weighted Bergman spaces $A_\mu ^p$, $1 < p < \infty $, on the disc. Using a decomposition of $A_\mu ^p$ into finite-dimensional subspaces the operator $T_a$ can be considered as a coefficient multiplier. This leads to new results on boundedness of $T_a$ and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of $T_a$ for $a$ satisfying an assumption on the positivity of certain indefinite integrals.