Boundedness of multidimensional hausdorff operators in h                         p                          spaces, 0 < p < 1

Elijah Liflyand; Akihiko Miyachi

doi:10.1090/tran/7572

Boundedness of multidimensional hausdorff operators in h ^p spaces, 0 < p < 1

Elijah Liflyand, Akihiko Miyachi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

Sufficient conditions, of both smoothness and algebraic type, for the boundedness of multidimensional Hausdorff operators in Hardy spaces Hp(Rn), n ≥ 2, 0 < p < 1, are given. Positive and negative examples illustrate all aspects of the behavior of such operators and reveal the special nature of the case p < 1.

Original language	English
Pages (from-to)	4793-4814
Number of pages	22
Journal	Transactions of the American Mathematical Society
Volume	371
Issue number	7
DOIs	https://doi.org/10.1090/tran/7572
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2018 American Mathematical Society.

Keywords

Atomic decomposition
Fourier transform
Hardy space
Hausdorff operator
Smoothness

Access to Document

10.1090/tran/7572

Cite this

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Boundedness of multidimensional hausdorff operators in h ^p spaces, 0 < p < 1 . / Liflyand, Elijah; Miyachi, Akihiko.
In: Transactions of the American Mathematical Society, Vol. 371, No. 7, 2019, p. 4793-4814.

Research output: Contribution to journal › Article › peer-review

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