Toeplitz operators on Bergman spaces and Hardy multipliers
Abstract. We study Toeplitz operators Ta with radial symbols in weighted Bergman spaces Aμ, 1 < p < ∞, on the disc. Using a decomposition of Aμ into finite dimensional subspaces the operator Ta can be considered as a coefficient multiplier. This leads to new results on boundedness of Ta and also shows a connection to Hardy space multipliers. Using another method we also prove a necessary and suffient condition for the boundedness of Ta for a satisfying an assumption on the positivity of certain indefinite integrals.
We study regularity properties of a positive measure in the euclidean space in terms of two square functions which are the multiplicative analogues of the usual martingale square function and of the Lusin area function of a harmonic function. The size of ...