Generalized Stević–Sharma Type Operators on Spaces of Fractional Cauchy Transforms

Let \({\mathbb {D}}=\{z \in {\mathbb {C}}: |z| < 1 \}\) $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ and \(\alpha >0\) $\alpha >0$ . Let \({\mathcal {F}}_{\alpha }\) ${\mathcal{F}}_{\alpha }$ be the collection of all holomorphic functions defined for \(z\in {\mathbb {D}}\) $z\in \mathbb{D}$ by integrating the kernel \((1-\overline{\zeta }z)^{-\alpha }\) ${(1-\overline{\zeta }z)}^{-\alpha }$ against a complex valued measure on the \({\mathbb {T}} = \partial {\mathbb {D}}\) $\mathbb{T}=\partial \mathbb{D}$ . Considering the generalized Stevic–Sharma type operator on \({\mathcal {F}}_{\alpha }\) ${\mathcal{F}}_{\alpha }$ , we find an estimate for the essential norm of the operator.