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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Harmonic Bergman Functions on Half-Spaces
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by Wade C. Ramey and HeungSu Yi PDF
Trans. Amer. Math. Soc. 348 (1996), 633-660 Request permission

Abstract:

We study harmonic Bergman functions on the upper half-space of $\mathbf {R}^n$. Among our main results are: The Bergman projection is bounded for the range $1< p < \infty$; certain nonorthogonal projections are bounded for the range $1\leq p < \infty$; the dual space of the Bergman $L^1$-space is the harmonic Bloch space modulo constants; harmonic conjugation is bounded on the Bergman spaces for the range $1\leq p < \infty$; the Bergman norm is equivalent to a “normal derivative norm” as well as to a “tangential derivative norm”.
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Additional Information
  • Wade C. Ramey
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
  • Email: ramey@math.msu.edu
  • HeungSu Yi
  • Affiliation: Global Analysis Research Center, Department of Mathematics, Seoul National University, Seoul, Korea #151-742
  • Email: hsyi@math.snu.ac.kr
  • Received by editor(s): October 13, 1994
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 633-660
  • MSC (1991): Primary 31B05; Secondary 31B10, 30D55, 30D45
  • DOI: https://doi.org/10.1090/S0002-9947-96-01383-9
  • MathSciNet review: 1303125