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Fourier multipliers on spaces of distributions

Published online by Cambridge University Press:  20 January 2009

W. Lamb
W. Lamb
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow
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In [8], Rooney defines a class of complex-valued functions ζ each of which is analytic in a vertical strip α(ζ)< Res < β(ζ) in the complex s-plane and satisfies certain growth conditions as |Im s| →∞ along fixed lines Re s = c lying within this strip. These conditions mean that the functions

fulfil the requirements of the one-dimensional Mihlin-Hörmander theorem (see [6, p. 417]) and so can be regarded as Fourier multipliers for the Banach spaces . Consequently, each function gives rise to a family of bounded operators W[ζ,σ] σ ∈(α(ζ),β(ζ)), on , 1<p<∞.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 3 , October 1986 , pp. 309 - 327
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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