Litte Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball

David Békollé; Hugues Olivier Defo; Edgar L. Tchoundja; Brett D. Wick

doi:10.1007/s00020-021-02640-w

Litte Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball

David Békollé
, Hugues Olivier Defo
, Edgar L. Tchoundja
, Brett D. Wick

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we study the boundedness and the compactness of the little Hankel operators h_b with operator-valued symbols b between different weighted vector-valued Bergman spaces on the open unit ball B_n in Cⁿ. More precisely, given two complex Banach spaces X, Y, and 0 < p, q≤ 1 , we characterize those operator-valued symbols b: B_n→ L(X¯ , Y) for which the little Hankel operator hb:Aαp(Bn,X)⟶Aαq(Bn,Y), is a bounded operator. Also, given two reflexive complex Banach spaces X, Y and 1 < p≤ q< ∞, we characterize those operator-valued symbols b: B_n→ L(X¯ , Y) for which the little Hankel operator hb:Aαp(Bn,X)⟶Aαq(Bn,Y), is a compact operator.

Original language	English
Article number	28
Journal	Integral Equations and Operator Theory
Volume	93
Issue number	3
DOIs	https://doi.org/10.1007/s00020-021-02640-w
State	Published - Jun 2021

Keywords

Little Hankel operator
Operator-valued symbol
Vector-valued Bergman spaces

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10.1007/s00020-021-02640-w

Cite this

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title = "Litte Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball",

abstract = "In this paper, we study the boundedness and the compactness of the little Hankel operators hb with operator-valued symbols b between different weighted vector-valued Bergman spaces on the open unit ball Bn in Cn. More precisely, given two complex Banach spaces X, Y, and 0 < p, q≤ 1 , we characterize those operator-valued symbols b: Bn→ L(X¯ , Y) for which the little Hankel operator hb:Aαp(Bn,X)⟶Aαq(Bn,Y), is a bounded operator. Also, given two reflexive complex Banach spaces X, Y and 1 < p≤ q< ∞, we characterize those operator-valued symbols b: Bn→ L(X¯ , Y) for which the little Hankel operator hb:Aαp(Bn,X)⟶Aαq(Bn,Y), is a compact operator.",

keywords = "Little Hankel operator, Operator-valued symbol, Vector-valued Bergman spaces",

author = "David B{\'e}koll{\'e} and Defo, \{Hugues Olivier\} and Tchoundja, \{Edgar L.\} and Wick, \{Brett D.\}",

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month = jun,

doi = "10.1007/s00020-021-02640-w",

language = "English",

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T1 - Litte Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball

AU - Békollé, David

AU - Defo, Hugues Olivier

AU - Tchoundja, Edgar L.

AU - Wick, Brett D.

PY - 2021/6

Y1 - 2021/6

N2 - In this paper, we study the boundedness and the compactness of the little Hankel operators hb with operator-valued symbols b between different weighted vector-valued Bergman spaces on the open unit ball Bn in Cn. More precisely, given two complex Banach spaces X, Y, and 0 < p, q≤ 1 , we characterize those operator-valued symbols b: Bn→ L(X¯ , Y) for which the little Hankel operator hb:Aαp(Bn,X)⟶Aαq(Bn,Y), is a bounded operator. Also, given two reflexive complex Banach spaces X, Y and 1 < p≤ q< ∞, we characterize those operator-valued symbols b: Bn→ L(X¯ , Y) for which the little Hankel operator hb:Aαp(Bn,X)⟶Aαq(Bn,Y), is a compact operator.

AB - In this paper, we study the boundedness and the compactness of the little Hankel operators hb with operator-valued symbols b between different weighted vector-valued Bergman spaces on the open unit ball Bn in Cn. More precisely, given two complex Banach spaces X, Y, and 0 < p, q≤ 1 , we characterize those operator-valued symbols b: Bn→ L(X¯ , Y) for which the little Hankel operator hb:Aαp(Bn,X)⟶Aαq(Bn,Y), is a bounded operator. Also, given two reflexive complex Banach spaces X, Y and 1 < p≤ q< ∞, we characterize those operator-valued symbols b: Bn→ L(X¯ , Y) for which the little Hankel operator hb:Aαp(Bn,X)⟶Aαq(Bn,Y), is a compact operator.

KW - Little Hankel operator

KW - Operator-valued symbol

KW - Vector-valued Bergman spaces

UR - https://www.scopus.com/pages/publications/85106268175

U2 - 10.1007/s00020-021-02640-w

DO - 10.1007/s00020-021-02640-w

M3 - Article

AN - SCOPUS:85106268175

SN - 0378-620X

VL - 93

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

M1 - 28

ER -

Litte Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball

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Keywords

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