Norm of a generalized Hilbert linear and bilinear form on the Hardy spaces

Norm of a generalized Hilbert linear and bilinear form on the Hardy spaces

In this paper, the precise norm of a generalized Hilbert linear form HLλ on the Hardy space H1 and that of the corresponding bilinear form HBλ on the Hardy space pair (Hp,Hq) are given for all λ∈{x∈R:x≠0,−1,−2,⋯}. Furthermore, the classical Hardy's inequality on the absolute convergence of HL1...

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Veröffentlicht in:Journal of mathematical analysis and applications 2025-01, Vol.541 (2), p.128724, Article 128724
1. Verfasser: Yang, Weifeng
Format: Artikel
Sprache:eng
Schlagworte:
Hankel form
Hardy space
Hilbert bilinear form
Hilbert inequality
Hilbert matrix operator
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Zusammenfassung:In this paper, the precise norm of a generalized Hilbert linear form HLλ on the Hardy space H1 and that of the corresponding bilinear form HBλ on the Hardy space pair (Hp,Hq) are given for all λ∈{x∈R:x≠0,−1,−2,⋯}. Furthermore, the classical Hardy's inequality on the absolute convergence of HL1 is generalized to all HLλ with λ>0.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128724