Norm of the Hausdorff Operator on the Real Hardy Space H1(R)

Let φ be a nonnegative integrable function on ( 0 , ∞ ) . It is well-known that the Hausdorff operator H φ generated by φ is bounded on the real Hardy space H 1 ( R ) . The aim of this paper is to give the exact norm of H φ . More precisely, we prove that ‖ H φ ‖ H 1 ( R ) → H 1 ( R ) = ∫ 0 ∞ φ ( t...

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Bibliographic Details
Published in:Complex analysis and operator theory 2018, Vol.12 (1), p.235-245
Main Authors: Duy Hung, Ha, Dang Ky, Luong, Thuan Quang, Thai
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Operator Theory
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Summary:Let φ be a nonnegative integrable function on ( 0 , ∞ ) . It is well-known that the Hausdorff operator H φ generated by φ is bounded on the real Hardy space H 1 ( R ) . The aim of this paper is to give the exact norm of H φ . More precisely, we prove that ‖ H φ ‖ H 1 ( R ) → H 1 ( R ) = ∫ 0 ∞ φ ( t ) d t .
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-017-0651-y