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

authored by

D. Békollè, T. Mfouapon, E. L. Tchoundja

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_αΦ¹(B_n,X)⟶A_αΦ²(B_n,Y), extends into a bounded operator, where Φ₁ and Φ₂ are either convex or concave growth functions.

Organisation(s)

Institute of Analysis

External Organisation(s)

University of Yaounde I

Type

Article

Journal

Analysis mathematica

Volume

50

Pages

31-78

No. of pages

48

ISSN

0133-3852

Publication date

03.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Analysis, Mathematics(all)

Electronic version(s)

https://doi.org/10.1007/s10476-024-00002-3 (Access: Closed)