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Spherical functions on harmonic extensions ofH-type groups

✍ Scribed by Anthony H. Dooley; Genkai Zhang

Publisher: Springer-Verlag
Year: 1999
Tongue: English
Weight: 436 KB
Volume: 9
Category: Article
ISSN: 1050-6926
DOI: 10.1007/bf02921938

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A growth lemma for certain discrete symmetric Laplacians defined on a lattice Z d δ = δZ d ⊂ R d with spacing δ is proved. The lemma implies a De Giorgi theorem, that the harmonic functions for these Laplacians are equi-Hölder continuous, δ → 0. These results are then applied to establish regularity