Bounded and compact multipliers between Bergman and Hardy spaces

Abstract

This paper studies the boundedness and compactness of the coefficient multiplier operators between various Bergman spacesA p and Hardy spacesH q. Some new characterizations of the multipliers between the spaces with exponents 1 or 2 are derived which, in particular, imply a Bergman space analogue of the Paley-Rudin Theorem on sparse sequences. Hardy and Bergman spaces are shown to be linked using mixed-norm spaces, and this linkage is used to improve a known result on (A p,A 2), 1<p<2.Compact (H 1,H 2) and (A 1,A 2) multipliers are characterized. The essential norms and spectra of some multiplier operators are computed. It is shown that forp>1 there exist bounded non-compact multiplier operators fromA p toA q if and only ifp≤q.