1. Coefficient multipliers in the Hardy space associated with Jacobi expansions.
- Author
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Shi, Yehao and Li, Zhongkai
- Subjects
SEQUENCE spaces ,MULTIPLIERS (Mathematical analysis) ,HARDY spaces ,GENERALIZATION ,MATHEMATICS - Abstract
In this paper a multiplier theorem in the Hardy space H^1(\mathbb {T}) associated with Jacobi expansions of exponential type is proved, that is, a bilateral sequence \left \{\lambda _n\right \}_{n=-\infty }^{\infty } is a multiplier from H^1(\mathbb {T}) into the sequence space \ell ^1(\mathbb {Z}) associated with Jacobi expansions of exponential type, if \[ \sup _N\sum _{k=1}^{\infty }\left (\sum _{kN<|j|\le (k+1)N}|\lambda _j|\right)^2<\infty.\] This is a generalization of a multiplier theorem on usual Fourier expansions in the Hardy space H^1(\mathbb {T}), and for \lambda _n=(|n|+1)^{-1}, a Hardy type inequality for Jacobi expansions is immediate which has ever been proved by Kanjin and Sato [Math. Inequal. Appl. 7 (2004), pp. 551–555]. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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