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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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On the mean value property of harmonic functions and best harmonic $L^ 1$-approximation
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by Myron Goldstein, Werner Haussmann and Lothar Rogge PDF
Trans. Amer. Math. Soc. 305 (1988), 505-515 Request permission


The present paper deals with the inverse mean value property of harmonic functions and with the existence, uniqueness, and characterization of a best harmonic ${L^1}$-approximant to strictly subharmonic functions. The main theorem concerning the inverse mean value property of harmonic functions is based on a generalization of a theorem due to Ü. Kuran as well as on an approximation theorem proved by J. C. Polking and also by L. I. Hedberg. The inverse mean value property will be applied in order to prove necessary and sufficient conditions for the existence of a best harmonic ${L^1}$-approximant to a subharmonic function $s$ satisfying $\Delta s > 0$ a.e. in the unit ball.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 305 (1988), 505-515
  • MSC: Primary 31B05; Secondary 41A30, 41A50
  • DOI:
  • MathSciNet review: 924767