# Little Hankel Operators between Bergman Spaces of the Right Half Plane

### New Zealand Journal of Mathematics

Vol. 38, (2008), Pages 99-119

N. Das

P. G. Dept. of Mathematics

Utkal University

Vanivihar

Bhubaneswar

751004, Orissa

INDIA

Abstract In this paper we consider a class of weighted integral operators on L2 (0, $\infty$) and show that they are unitarily equivalent to little Hankel operators between weighted Bergman spaces of the right half plane. We use two parameters $\alpha, \beta \in (-1, \infty)$ and involve two weights to define Bergman spaces of the domain and range of the little Hankel operators. We obtained conditions for the Hankel integral operator to be Hilbert-Schmidt, nuclear, finite rank and compact, expressed in terms of the kernel of the integral operator. For certain class of weights, these operators are shown to be unitarily equivalent to little Hankel operators between weighted Bergman spaces of the disk, and the symbol correspondence is given. In view of the strong link between Hankel operators and best approximation, some asymptotic results on the singular values of Hankel integral operators are also provided.

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Classification (MSC2000)