## Details

Original language | English |
---|---|

Pages (from-to) | 31-78 |

Number of pages | 48 |

Journal | Analysis mathematica |

Volume | 50 |

Issue number | 1 |

Early online date | 13 Mar 2024 |

Publication status | Published - Mar 2024 |

## Abstract

In this paper, we consider vector-valued Bergman–Orlicz spaces which are generalization of classical vector-valued Bergman spaces. We characterize the dual space of vector-valued Bergman–Orlicz space, and study the boundedness of the little Hankel operators, h_{b}, with operator-valued symbols b, between different weighted vector-valued Bergman–Orlicz spaces on the unit ball B_{n}.More precisely, given two complex Banach spaces X, Y, we characterize those operator-valued symbolsb:B_{n}→L(X¯,Y) for which the little Hankel operator h_{b}:A_{α}Φ^{1}(B_{n},X)⟶A_{α}Φ^{2}(B_{n},Y), extends into a bounded operator, where Φ_{1} and Φ_{2} are either convex or concave growth functions.

## Keywords

- little Hankel operator, operator-valued symbol, vector-valued Bergman–Orlicz space, 47B90, 32A36, 32A10, 46E40

## ASJC Scopus subject areas

- Mathematics(all)
**Analysis****Mathematics(all)**

## Cite this

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**Duality for vector-valued Bergman–Orlicz spaces and little Hankel operators between vector-valued Bergman–Orlicz spaces on the unit ball.**/ Békollè, D.; Mfouapon, T.; Tchoundja, E. L.

In: Analysis mathematica, Vol. 50, No. 1, 03.2024, p. 31-78.

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

*Analysis mathematica*, vol. 50, no. 1, pp. 31-78. https://doi.org/10.1007/s10476-024-00002-3

*Analysis mathematica*,

*50*(1), 31-78. https://doi.org/10.1007/s10476-024-00002-3

}

TY - JOUR

T1 - Duality for vector-valued Bergman–Orlicz spaces and little Hankel operators between vector-valued Bergman–Orlicz spaces on the unit ball

AU - Békollè, D.

AU - Mfouapon, T.

AU - Tchoundja, E. L.

PY - 2024/3

Y1 - 2024/3

N2 - In this paper, we consider vector-valued Bergman–Orlicz spaces which are generalization of classical vector-valued Bergman spaces. We characterize the dual space of vector-valued Bergman–Orlicz space, and study the boundedness of the little Hankel operators, hb, with operator-valued symbols b, between different weighted vector-valued Bergman–Orlicz spaces on the unit ball Bn.More precisely, given two complex Banach spaces X, Y, we characterize those operator-valued symbolsb:Bn→L(X¯,Y) for which the little Hankel operator hb:AαΦ1(Bn,X)⟶AαΦ2(Bn,Y), extends into a bounded operator, where Φ1 and Φ2 are either convex or concave growth functions.

AB - In this paper, we consider vector-valued Bergman–Orlicz spaces which are generalization of classical vector-valued Bergman spaces. We characterize the dual space of vector-valued Bergman–Orlicz space, and study the boundedness of the little Hankel operators, hb, with operator-valued symbols b, between different weighted vector-valued Bergman–Orlicz spaces on the unit ball Bn.More precisely, given two complex Banach spaces X, Y, we characterize those operator-valued symbolsb:Bn→L(X¯,Y) for which the little Hankel operator hb:AαΦ1(Bn,X)⟶AαΦ2(Bn,Y), extends into a bounded operator, where Φ1 and Φ2 are either convex or concave growth functions.

KW - little Hankel operator

KW - operator-valued symbol

KW - vector-valued Bergman–Orlicz space

KW - 47B90

KW - 32A36

KW - 32A10

KW - 46E40

UR - http://www.scopus.com/inward/record.url?scp=85187677103&partnerID=8YFLogxK

U2 - 10.1007/s10476-024-00002-3

DO - 10.1007/s10476-024-00002-3

M3 - Article

AN - SCOPUS:85187677103

VL - 50

SP - 31

EP - 78

JO - Analysis mathematica

JF - Analysis mathematica

SN - 0133-3852

IS - 1

ER -