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Projections on Bergman Spaces Over Plane Domains

Published online by Cambridge University Press:  20 November 2018

Jacob Burbea
Jacob Burbea*
Affiliation:
University of Pittsburgh, Pittsburgh, Pennsylvania
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Let D be a bounded plane domain and let Lp(D) stand for the usual Lebesgue spaces of functions with domain D, relative to the area Lebesque measure dσ(z) = dxdy. The class of all holomorphic functions in D will be denoted by H(D) and we write Bp(D) = Lp(D) ∩ H(D). Bp(D) is called the Bergman p-space and its norm is given by

Let be the Bergman kernel of D and consider the Bergman projection

(1.1)

It is well known that P is not bounded on Lp(D), p = 1, ∞, and moreover, it can be shown that there are no bounded projections of L∞(Δ) onto B∞(Δ).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 6 , 01 December 1979 , pp. 1269 - 1280
Copyright
Copyright © Canadian Mathematical Society 1979

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