Buckley, Stephen M. and Ramanujan, M.S. and Vukotić, Dragan
(1999)
Bounded and compact multipliers between Bergman and Hardy Spaces.
Integral Equations and Operator Theory, 35 (1).
pp. 119.
ISSN 14208989
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 PaleyRudin Theorem on sparse sequences. Hardy and Bergman spaces are shown to be linked using mixednorm 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 noncompact multiplier operators from
Ap to Aq if and only if p≤q.
Item Type: 
Article

Additional Information: 
The original publication is available at http://www.springerlink.com/content/p21611821x26nu79/fulltext.pdf 
Keywords: 
Bergman spaces; Hardy spaces; PaleyRudin Theorem; Boundedness; Compactness. 
Academic Unit: 
Faculty of Science and Engineering > Mathematics and Statistics 
Item ID: 
1614 
Identification Number: 
10.1007/BF01225524 
Depositing User: 
Prof. Stephen Buckley

Date Deposited: 
21 Oct 2009 12:43 
Journal or Publication Title: 
Integral Equations and Operator Theory 
Publisher: 
Birkhäuser Basel 
Refereed: 
No 
URI: 

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