Bounded and compact multipliers between Bergman and Hardy spaces |
| |
Authors: | Stephen M Buckley M S Ramanujan Dragan Vukotić |
| |
Institution: | (1) Department of Mathematics, National University of Ireland Maynooth, Co., Kildare, Ireland;(2) Departmento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain;(3) Department of Mathematics, The University of Michigan, 48109-1109 Ann Arbor, MI, USA |
| |
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 ifpq. |
| |
Keywords: | Primary 47B38 Secondary 30B10 46E15 |
本文献已被 SpringerLink 等数据库收录! |
|