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Multidimensional Hausdorff operators on the real Hardy space

Part of: Harmonic analysis in several variables Linear function spaces and their duals Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

A. K. Lerner  and
E. Liflyand
A. K. Lerner
Affiliation:
Department of MathematicsBar-Ilan University52900 [email protected], [email protected]
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Abstract

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For a wide family of multivariate Hausdorff operators, the boundedness of an operator from this family i s proved on the real Hardy space. By this we extend and strengthen previous results due to Andersen and Móricz.

Keywords

Hausdorff operatorFourier transformreal Hardy space

MSC classification

Secondary: 47B38: Operators on function spaces (general) 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 1 , August 2007 , pp. 79 - 86
Copyright
Copyright © Australian Mathematical Society 2007

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