Boundeness of a family of Hilbert-type operators and of its Bergman-type analogue

2015/12/08 by Justice Sam Bansah, Justice S. Bansah, Bansah, Justice S. +3 · 2 citations
Mathematics · #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.CA #math.CV #math.FA #msc:26D15 #msc:28A25 #msc:47B34

paper · pdf · doi:10.48550/arxiv.1512.02537

arxiv created 2016/01/08 · arxiv updated 2016/01/11

Abstract

In this note, we frst consider boundedness properties of a family of operators generalizing the Hilbert operator in the upper triangle case. In the diagonal case, we give the exact norm of these operators under some restrictions on the parameters. We secondly consider boundedness properties of a family of positive Bergman-type operators of the upper-half plane. We give necessary and sufficient conditions on the parameters under which these operators are bounded in the upper triangle case.

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