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Journal of Function Spaces and Applications
Volume 4, Issue 3, Pages 305-327

N-harmonic extensions of weighted integrable distributions

1Department of Mathematics, New Mexico State University, Las Cruces, NM 88003, USA
2Departamento de Matemáticas, Universidad de Sonora, Hermosillo, Sonora 83000, México
3Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, Cuernavaca, Morelos 62251, México

Received 1 March 2006

Academic Editor: Hans Triebel

Copyright © 2006 Hindawi Publishing Corporation. 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.


We obtain n-harmonic extensions to the Cartesian product of ncopies of the upper half-plane, of distributions in the weighted space w12?wn2DL1', which is known to be the optimal space of tempered distributions that are S'-convolvable with a natural product domain version of the Poisson kernel.