Korányi's lemma for homogeneous Siegel domains of type II. Applications and extended results

Authors

  • D. Bekolle University of Ngaoundere, Faculty of Science, Department of Mathematics and Computer Science, PO Box 454, Ngaoundere
  • H. Ishi School of Mathematics, Nagoya University, Furo-Cho, Chikusa-Ku, Nagoya 464-8602
  • C. Nana University of Buea, Faculty of Science, Department of Mathematics, PO Box 63, Buea

Keywords:

Homogeneous Siegel domain of type II, Bergman kernel, Bergman metric, Bergman mapping, Bergman space, Bergman projector, atomic decomposition, interpolation.

Abstract

We show that the modulus of the Bergman kernel B(z, ζ) of a general homogeneous Siegel domain of type II is â€almost constant†uniformly with respect to z when ζ varies inside a Bergman ball. The control is expressed in terms of the Bergman distance. This result was proved by A. Korányi for symmetric Siegel domains of type II. Subsequently, R. R. Coifman and R. Rochberg used this result to establish an atomic decomposition theorem and an interpolation theorem by functions in Bergman spaces \(A^p\) on these domains. The atomic decomposition theorem and the interpolation theorem are extended here to the general homogeneous case using the same tools. We further extend the range of exponents \(p\) via functional analysis using recent estimates. DOI: 10.1017/S0004972714000033

Published

2014-06-03

Issue

Vol. 90 No. 1 (2014)

Section

Articles
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