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On the p-norm of the truncated n-dimensional Hilbert transform

Published online by Cambridge University Press:  17 April 2009

J.N. Pandey  and
O.P. Singh
J.N. Pandey
Affiliation:
Department of Mathematics and Statistcs, Carleton University Ottawa, CanadaK1S 5B6
O.P. Singh
Affiliation:
Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi - 221005, India
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Abstract

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It is shown that a bounded linear operator T from Lρ(Rn) to itself which commutes both with translations and dilatations is a finite linear combination of Hilbert-type transforms. Using this we show that the ρ-norm of the Hilbert transform is the same as the ρ-norm of its truncation to any Lebesgue measurable subset of Rn with non-zero measure.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 2 , April 1991 , pp. 241 - 250
Copyright
Copyright © Australian Mathematical Society 1991

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