Multipliers of Laplace transform type for ultraspherical expansions

✍ Scribed by Teresa Martinez

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 173 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200610654

✦ Synopsis

Abstract

We define and investigate the multipliers of Laplace transform type associated to the differential operator L~λ~f (θ) = –f ″(θ) – 2__λ__ cot θf ′(θ) + λ^2^f (θ), λ > 0. We prove that these operators are bounded in L^p^ ((0, π), dm~λ~) and of weak type (1, 1) with respect to the same measure space, dm~λ~ (θ) = (sin θ)^2__λ__^ dθ. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)