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Multipliers of Laplace transform type for ultraspherical expansions
Author(s) -
Martinez Teresa
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610654
Subject(s) - mathematics , laplace transform , bounded function , type (biology) , operator (biology) , space (punctuation) , differential operator , measure (data warehouse) , mathematical analysis , pure mathematics , chemistry , ecology , biochemistry , repressor , database , gene , transcription factor , computer science , biology , linguistics , philosophy
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)
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