Weierstrass transform associated with the Hankel operator.
Let Ω be a bounded strictly pseudoconvex domain in . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection belong to the Hardy-Sobolev space . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space .
The boundedness, compactness and closedness of the range of weighted composition operators acting on weighted Lorentz spaces L(p,q,wdμ) for 1 < p ≤ ∞, 1 ≤ q ≤ ∞ are characterized.
We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class . The main tool is a discretization in terms of an almost orthogonal wavelet expansion adapted to the radial situation.
We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.