## Hiroshima Mathematical Journal

### Atomic decomposition of harmonic Bergman functions

Kiyoki Tanaka

#### Abstract

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

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

Dates
First available in Project Euclid: 20 August 2012

https://projecteuclid.org/euclid.hmj/1345467067

Digital Object Identifier
doi:10.32917/hmj/1345467067

Mathematical Reviews number (MathSciNet)
MR2978299

Zentralblatt MATH identifier
1250.31005

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

#### Citation

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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