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On the Range and Invertibility of a Class of Melon Multiplier Transforms III

Published online by Cambridge University Press:  20 November 2018

A. C. McBride  and
W. J. Spratt
A. C. McBride
Affiliation:
Department of Mathematics, University of Strathclyde, LivingstoneTower, 26 Richmond Street, Glasgow Gl 1XH, Scotland
W. J. Spratt
Affiliation:
12 Hickory Close, Lytchett Minster, Poole, Dorset, England
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Abstract

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We continue to develop the theory of previous papers concerning transforms corresponding to Mellin multipliers which involve products and/or quotients of Γ-functions. We show that, by working with certain subspaces of Lp,μ consisting of smooth functions, we can simplify considerably the restrictions on the parameters which were necessary in the Lp,μ setting. As a result, operators in our class become homeomorphisms on these subspaces under conditions of great generality.

Keywords

42A4544A15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 6 , 01 December 1991 , pp. 1323 - 1338
Copyright
Copyright © Canadian Mathematical Society 1991

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