Abstract

This paper studies the boundedness and compactness of the coefficient multiplier operators between various Bergman spaces Ap and Hardy spaces Hq. 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 for p>1 there exist bounded non-compact multiplier operators from Ap to Aq if and only if p≤q.