Abstract
The purpose is to provide a generalization of Carleson's Theorem on interpolating sequences when dealing with a sequence in the open unit ball of a Hilbert space. Precisely, we interpolate a sequence by a function belonging to a weighted Bergman space of infinite order on a unit Hilbert ball and we furnish explicitly the upper bound corresponding to the interpolation constant.
Keywords
Interpolation sequences weighted Bergman spaces pseudohyberbolic distance Fréchet differentiable functions. Analytic functions
References
- K. M. Dyakonov: A free interpolation problem for a subspace of $H^\infty$, Bull Lond Math Soc., 50 (2018), 477–486.
- B. Berndtsson: Interpolating sequences for $H^\infty$ in the ball, Nederl Akad Wetensch Indag Math., 47 (1) (1985), 1-10.
- M. El Aïdi: On the interpolation constant for weighted Bergman spaces of infinite order, Complex Var. Elliptic Equ., 64 (6) (2019), 1043–1049.
- P. Galindo, A. Miralles: Interpolating sequences for bounded analytic functions, Proc Amer Math Soc., 135 (10) (2007), 3225–3231.
- K. Goebel, S. Reich: Uniform convexity, hyperbolic geometry, and nonexpansive mappings, Marcel Dekker, Inc., New York and Basel, 1984.
- P. Jones: $L^\infty$-estimates for the $\delta$ problem in a half-plane, Acta Math., 150 (1983) 137–152.
- X. Massaneda: Interpolation by holomorphic functions in the unit ball with polynomial growth Ann Fac Sci Toulouse Math., 6 (2) (1997), 277–296.
- A. Miralles: Interpolating sequences for $H^\infty(B_H)$, Quaest Math., 39 (6) (2016), 785–795.
- T. T. Quang: Banach-valued Bloch-type functions on the unit ball of a Hilbert space and weak spaces of Bloch-type, Constr. Math. Anal., 6 (1) (2023), 6–21.
Abstract
References
- K. M. Dyakonov: A free interpolation problem for a subspace of $H^\infty$, Bull Lond Math Soc., 50 (2018), 477–486.
- B. Berndtsson: Interpolating sequences for $H^\infty$ in the ball, Nederl Akad Wetensch Indag Math., 47 (1) (1985), 1-10.
- M. El Aïdi: On the interpolation constant for weighted Bergman spaces of infinite order, Complex Var. Elliptic Equ., 64 (6) (2019), 1043–1049.
- P. Galindo, A. Miralles: Interpolating sequences for bounded analytic functions, Proc Amer Math Soc., 135 (10) (2007), 3225–3231.
- K. Goebel, S. Reich: Uniform convexity, hyperbolic geometry, and nonexpansive mappings, Marcel Dekker, Inc., New York and Basel, 1984.
- P. Jones: $L^\infty$-estimates for the $\delta$ problem in a half-plane, Acta Math., 150 (1983) 137–152.
- X. Massaneda: Interpolation by holomorphic functions in the unit ball with polynomial growth Ann Fac Sci Toulouse Math., 6 (2) (1997), 277–296.
- A. Miralles: Interpolating sequences for $H^\infty(B_H)$, Quaest Math., 39 (6) (2016), 785–795.
- T. T. Quang: Banach-valued Bloch-type functions on the unit ball of a Hilbert space and weak spaces of Bloch-type, Constr. Math. Anal., 6 (1) (2023), 6–21.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Early Pub Date | June 4, 2023 |
| Publication Date | June 15, 2023 |
| Published in Issue | Year 2023 Volume: 6 Issue: 2 |
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