Convolution operators on Lorentz spaces over locally compact Vilenkin groups

✍ Scribed by T. S. Quek

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 182 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200510601

✦ Synopsis

Abstract

Let G be a locally compact Vilenkin group. Using Herz spaces, we give sufficient conditions for a distribution on G to be a convolution operator on certain Lorentz spaces. Our results generalize Hörmander's multiplier theorem on G. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)