Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T23:38:58.964Z Has data issue: false hasContentIssue false
  • English
  • Français

Multipliers for the Mellin Transformation

Published online by Cambridge University Press:  20 November 2018

P. G. Rooney
P. G. Rooney*
Affiliation:
University of Toronto, Toronto, Ontario
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we generalize the Mellin multiplier theorem we proved earlier [8] to spaces with quite general weights, satisfying an Ap-type condition. Applications are made to the Hilbert transformation.

Keywords

42A1844A15multipliersMellin transformationHilbert transformation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 3 , 01 September 1982 , pp. 257 - 262
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Andersen, K. F., Weighted norm inequalities for Hilbert transforms and conjugate functions of even and odd functions, Proc. Amer. Math. Soc. 56 (1976), 99-107.Google Scholar
2. Erdélyi, A. et al, Higher transcendental functions I, New York (McGraw-Hill), 1953.Google Scholar
3. Hunt, R., B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251.Google Scholar
4. Kurtz, D. S., Littlewood-Paley and multiplier theorems on weighted Lp spaces, Trans. Amer. Math. Soc. 259 (1980), 235-254.Google Scholar
5. Muckenhoupt, B., Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.Google Scholar
6. Muckenhoupt, B. and Stein, E. M., Classical expansions and their relations to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92.Google Scholar
7. Rooney, P. G., On the ranges of certain fractional integrals, Can. J. Math. 24 (1972), 1198-1216.Google Scholar
8. Rooney, P. G., A technique for studying the boundedness and extendability of certain types of operators, Can. J. Math. 25 (1973), 1090-1112.Google Scholar
9. Rudin, W., Real and complex analysis, 2nd ed., New York (McGraw-Hill), 1974.Google Scholar
10. Stein, E. M., Singular integrals, Princeton, 1970.Google Scholar