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On the p-norm of the truncated n-dimensional Hilbert transform
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1991
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