International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 625-640

The atomic decomposition of harmonic functions satisfying certain conditions of integrability

Krzysztof Bogdan

Institute of Mathematics, Technical University of Wroclaw, Wybrzeże Wyspiańskiego 27, Wrocław 50-370, Poland

Received 28 September 1992; Revised 3 May 1993

Copyright © 1995 Krzysztof Bogdan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Distributions on Euclidean spaces with derivatives of their Poisson integral satisfying certain natural conditions of integrability are represented as sums of weighted atoms. The atomic decomposition is obtained by means of the Calderón reproducing formula.