Commutativity and spectral properties of $k^{th}$-order slant little Hankel operators on the Bergman space

Abstract

In this paper, we introduce the notion of $k^{th}$-order slant little Hankel operator on the Bergman space with essentially bounded harmonic symbols on the unit disc and obtain its algebraic and spectral properties. We have also discussed the conditions under which $k^{th}$-order slant little Hankel operators commute.