𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Harmonic functions on the real hyperbolic ball II Hardy-Sobolev and Lipschitz spaces

✍ Scribed by Sandrine Grellier; Philippe Jaming

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
309 KB
Volume
268
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper, we pursue the study of harmonic functions on the real hyperbolic ball started in [13]. Our focus here is on the theory of Hardy‐Sobolev and Lipschitz spaces of these functions. We prove here that these spaces admit Fefferman‐Stein like characterizations in terms of maximal and square functionals. We further prove that the hyperbolic harmonic extension of Lipschitz functions on the boundary extend into Lipschitz functions on the whole ball. In doing so, we exhibit differences of behaviour of derivatives of harmonic functions depending on the parity of the dimension of the ball and on the parity of the order of derivation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Heat and Harmonic Extensions for Functio
Heat and Harmonic Extensions for Function Spaces of Hardy–Sobolev–Besov Type on Symmetric Spaces and Lie Groups
✍ Leszek Skrzypczak 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 192 KB

Function spaces of Hardy Sobolev Besov type on symmetric spaces of noncompact type and unimodular Lie groups are investigated. The spaces were originally defined by uniform localization. In the paper we give a characterization of the space F s p, q (X ) and B s p, q (X ) in terms of heat and Poisson