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Multipliers for semigroups

Published online by Cambridge University Press:  20 January 2009

G. Blower
G. Blower
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England
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Abstract

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Let L be a positive invertible self-adjoint operator in L2(X;C). Using transference methods for locally bounded groups of operators we obtain multipliers for the group of complex powers Liu on vector-valued Lebesgue spaces. Using a Mellin inversion formula, we derive a sufficient condition for a function to be a multiplier of the semigroup e-tL on Lp(X;E) where E is a UMD Banach space and 1<p<∞.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 241 - 252
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Berkson, E., Gillespie, T. A. and Muhly, P. S., Abstract spectral decompositions guaranteed by the Hilbert transform, Proc. London Math. Soc. (3) 53 (1986), 489–517.CrossRefGoogle Scholar
2. Chernoff, P. R., Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Anal. 12 (1973), 401–414.CrossRefGoogle Scholar
3. Guerre-Delabriere, S., Some remarks on complex powers of ( – Δ) and UMD spaces, Illinois J. Math. 35 (1991), 401–407.CrossRefGoogle Scholar
4. Hille, E. and Phillips, R. S. Functional analysis and semi-groups (American Math. Soc., Colloquium Publications, Vol. XXXI, Providence, R.I., 1957).Google Scholar
5. Mcconnell, T. R., On Fourier multiplier transformations of Banach-valued functions, Trans. Amer. Math. Soc. 285 (1984), 739–757.CrossRefGoogle Scholar
6. Sneddon, I. N. The use of integral transforms (McGraw-Hill, New York, 1972).Google Scholar
7. Stein, E. M. Topics in harmonic analysis related to the Littlewood Paley Theory (Annals of Math. Studies 63, Princeton, New Jersey, 1970).Google Scholar
8. Titchmarsh, E. C. The theory of functions, second edition (OUP, Oxford, 1938).Google Scholar