Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-02T22:22:12.712Z Has data issue: false hasContentIssue false

Bilateral Laplace multipliers on spaces of distributions

Published online by Cambridge University Press:  20 January 2009

S. E. Schiavone
Affiliation:
Department of MathematicsUniversity of AlbertaEdmonton, Alberta T6G 2G1, Canada
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.

A bilateral Laplace multiplier theory, based on Rooney's class , is developed for certain operators defined on the Fréchet spaces Dp,μ. The theory is applied to Riesz fractional integrals associated with the one-dimensional wave operator.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Lamb, W., Fourier multipliers on spaces of distributions, Proc. Edinburgh Math. Soc. 29 (1986), 309327.CrossRefGoogle Scholar
2.Mcbride, A. C., Fractional powers of a class of Mellin multiplier transforms I/II/III, Appl. Anal. 21 (1986), 89127/129–149/151–173.CrossRefGoogle Scholar
3.Mcbride, A. C. and Roach, G. F. (editors), Fractional Calculus (Research Notes in Mathematics, 138 (Pitman, London, 1985).Google Scholar
4.Okikiolu, G. O., Aspects of the theory of bounded integral operators in Lp-spaces (Academic Press, London, 1971).Google Scholar
5.Rooney, P. G., A technique for studying the boundedness and extendability of certain types of operators, Canad. J. Math. 25 (1973), 10901102.CrossRefGoogle Scholar
6.Schiavone, S. E. and Lamb, W., A fractional power approach to fractional calculus, J. Math. Anal. Appl., to appear.Google Scholar
7.Schwartz, L., Théorie des Distributions (nouvelle edn.) (Hermann, Paris, 1966).Google Scholar
8.Stein, E. M., Singular Integrals and Differentiability Properties of Functions (Princeton University Press, 1970).Google Scholar
9.Trèves, F., Topological Vector Spaces, Distributions and Kernels (Pure and Applied mathematics: A series of monographs and textbooks 25, Academic Press, New York, 1967).Google Scholar
10.Yosida, K., Functional Analysis (fifth edn.) (Springer-Verlag, Berlin, 1978).CrossRefGoogle Scholar