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On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball

Yıl 2023, , 102 - 106, 15.06.2023
https://doi.org/10.33205/cma.1240126

Öz

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.

Kaynakça

  • 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.
Yıl 2023, , 102 - 106, 15.06.2023
https://doi.org/10.33205/cma.1240126

Öz

Kaynakça

  • 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.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Mohammed El Aıdı 0000-0002-3032-0879

Erken Görünüm Tarihi 4 Haziran 2023
Yayımlanma Tarihi 15 Haziran 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA El Aıdı, M. (2023). On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball. Constructive Mathematical Analysis, 6(2), 102-106. https://doi.org/10.33205/cma.1240126
AMA El Aıdı M. On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball. CMA. Haziran 2023;6(2):102-106. doi:10.33205/cma.1240126
Chicago El Aıdı, Mohammed. “On an Interpolation Sequence for a Weighted Bergman Space on a Hilbert Unit Ball”. Constructive Mathematical Analysis 6, sy. 2 (Haziran 2023): 102-6. https://doi.org/10.33205/cma.1240126.
EndNote El Aıdı M (01 Haziran 2023) On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball. Constructive Mathematical Analysis 6 2 102–106.
IEEE M. El Aıdı, “On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball”, CMA, c. 6, sy. 2, ss. 102–106, 2023, doi: 10.33205/cma.1240126.
ISNAD El Aıdı, Mohammed. “On an Interpolation Sequence for a Weighted Bergman Space on a Hilbert Unit Ball”. Constructive Mathematical Analysis 6/2 (Haziran 2023), 102-106. https://doi.org/10.33205/cma.1240126.
JAMA El Aıdı M. On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball. CMA. 2023;6:102–106.
MLA El Aıdı, Mohammed. “On an Interpolation Sequence for a Weighted Bergman Space on a Hilbert Unit Ball”. Constructive Mathematical Analysis, c. 6, sy. 2, 2023, ss. 102-6, doi:10.33205/cma.1240126.
Vancouver El Aıdı M. On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball. CMA. 2023;6(2):102-6.