Computational Methods and Function Theory 7 (2007), No. 2, 429--432
Copyright Heldermann Verlag 2007
David A. Redett
redettd@ipfw.edu , Department of Mathematical Sciences, Indiana University--Purdue University, Fort Wayne, Indiana 46805, U.S.A.
A function f holomorphic in the unit disk D is called strongly annular if there exists a sequence of concentric circles in D expanding out to the unit circle such that f goes to infinity as |z| goes to 1 through these circles. It follows from the definition that if f has a radial limit, the limit must be infinity. It is clear from this observation that no function in the classical Hardy spaces can be strongly annular. We show in this note that there are strongly annular functions in Bergman space. We give a construction involving lacunary series.
Keywords: Bergman space, annular functions, boundary behavior.
MSC 2000: Primary 46E15, 30B30.
[FullText-pdf (181 K)] [FullText-ps (309 K)]