Hiroshima Mathematical Journal

Atomic decomposition of harmonic Bergman functions

Kiyoki Tanaka

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We consider harmonic Bergman functions, i.e., functions which are harmonic and $p$-th integrable. In the present paper, we shall show that when $10p0\infty$, every harmonic Bergman function on a smooth domain is represented as a series using the harmonic Bergman kernel. This representation is called an atomic decomposition.

Article information

Hiroshima Math. J., Volume 42, Number 2 (2012), 143-160.

First available in Project Euclid: 20 August 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 31B10: Integral representations, integral operators, integral equations methods
Secondary: 32A36: Bergman spaces

Harmonic Bergman space atomic decomposition


Tanaka, Kiyoki. Atomic decomposition of harmonic Bergman functions. Hiroshima Math. J. 42 (2012), no. 2, 143--160. doi:10.32917/hmj/1345467067. https://projecteuclid.org/euclid.hmj/1345467067

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