$\mu$-Hankel Operators on Compact Abelian Groups

Abstract

$(\mu ;\nu )$-Hankel operators between separable Hilbert spaces were introduced and studied recently (\textit{$\mu$-Hankel operators on Hilbert spaces}, Opuscula Math., \textbf{41} (2021), 881--899). This paper, is devoted to generalization of $(\mu ;\nu )$-Hankel operators to the (non-separable in general) case of Hardy spaces over compact and connected Abelian groups. In this setting bounded $(\mu ;\nu )$-Hankel operators are fully described under some natural conditions. Examples of integral operators are considered.