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Integr. equ. oper. theory 99 (9999), 119 0378-620X/99000-0, DOI 10.1007/s00020-003-0000

Summary: Integr. equ. oper. theory 99 (9999), 1­19
0378-620X/99000-0, DOI 10.1007/s00020-003-0000
c 2009 Birkh¨auser Verlag Basel/Switzerland
Integral Equations
and Operator Theory
Weighted Composition Operators from H
the Bloch Space of a Bounded Homogeneous
Robert F. Allen and Flavia Colonna
Abstract. Let D be a bounded homogeneous domain in Cn
. In this paper, we
study the bounded and the compact weighted composition operators mapping
the Hardy space H
(D) into the Bloch space of D. We characterize the
bounded weighted composition operators, provide operator norm estimates,
and give sufficient conditions for compactness. We prove that these conditions
are necessary in the case of the unit ball and the polydisk. We then show that
if D is a bounded symmetric domain, the bounded multiplication operators
from H


Source: Allen, Robert F. - Mathematics Department, University of Wisconsin-La Crosse


Collections: Mathematics