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A Note about Multi-Hilbert Transform on D(ℝ n )

A Note about Multi-Hilbert Transform on D(ℝ n ) In this paper, we first prove that, for a non-zero function f∈D(ℝ n ), its multi-Hilbert transform Hnf is bounded and does not have compact support. In addition, a new distribution space D' H (ℝ n ) is constructed and the definition of the multi-Hilbert transform is extended to it. It is shown that D' H (ℝ n ) is the biggest subspace of D'(ℝ n ) on which the extended multi-Hilbert transform is a homeomorphism. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A Note about Multi-Hilbert Transform on D(ℝ n )

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-018-0761-y
Publisher site
See Article on Publisher Site

Abstract

In this paper, we first prove that, for a non-zero function f∈D(ℝ n ), its multi-Hilbert transform Hnf is bounded and does not have compact support. In addition, a new distribution space D' H (ℝ n ) is constructed and the definition of the multi-Hilbert transform is extended to it. It is shown that D' H (ℝ n ) is the biggest subspace of D'(ℝ n ) on which the extended multi-Hilbert transform is a homeomorphism.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Apr 26, 2018

References