Generalized Hausdorff operator on Bergmann spaces

Abstract

Abstract In this article, we considered the generalized Hausdorff operator ℋ μ , ϕ , a {{\mathcal{ {\mathcal H} }}}_{\mu ,\phi ,a} on Bergmann space and determined the conditions on ϕ \phi and a a so that the operator is bounded. In addition, we studied the action of the Hausdorff operator on the truncated domain to estimate norm ℋ μ , ϕ , a {{\mathcal{ {\mathcal H} }}}_{\mu ,\phi ,a} and established a relation with quasi-Hausdorff operator on Bergmann space.