Generalized Hausdorff operator on Bergmann spaces

Abstract

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

Keywords

• hausdorff matrix
• cesàro operator
• bergmann spaces
• primary 47b38
• secondary 46e15