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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A Sobolev inequality for pluriharmonic functions
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by Steven R. Bell PDF
Proc. Amer. Math. Soc. 85 (1982), 350-352 Request permission

Abstract:

A Sobolev inequality is proved which implies that, on a smooth bounded domain $D$ contained in ${{\mathbf {C}}^n}$, the ${L^2}$ inner product of two pluriharmonic functions is defined whenever one of them is in ${C^\infty }(D)$ and the other is dominated by some negative power of the distance to the boundary.
References
  • Steven R. Bell, Biholomorphic mappings and the $\bar \partial$-problem, Ann. of Math. (2) 114 (1981), no. 1, 103–113. MR 625347, DOI 10.2307/1971379
  • Steven R. Bell, Proper holomorphic mappings and the Bergman projection, Duke Math. J. 48 (1981), no. 1, 167–175. MR 610182
  • Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, vol. 3, American Mathematical Society, Providence, R.I., 1979. With supplements by Lars Gȧrding and A. N. Milgram; With a preface by A. S. Householder; Reprint of the 1964 original. MR 598466
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 350-352
  • MSC: Primary 32A40; Secondary 31C10
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0656100-3
  • MathSciNet review: 656100