Generalized Hilbert matrix operators acting on weighted sequence spaces

Abstract In this paper, we introduce and study a new kind of generalized Hilbert matrix operators, induced by a positive finite Borel measure on left parenthesis 0 comma 1 right parenthesis $(0,1)$ <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content" display="inline"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , acting on weighted sequence spaces. We establish a sufficient and necessary condition for the boundedness of these operators. These results extend some related ones obtained recently in [ Bull. Lond. Math. Soc. 55(6) (2023), 2598–2610].