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.
"Atomic decomposition of harmonic Bergman functions." Hiroshima Math. J. 42 (2) 143 - 160, July 2012. https://doi.org/10.32917/hmj/1345467067