PRODUCT-TYPE OPERATORS FROM AREA NEVANLINNA SPACES TO BLOCH-ORLICZ SPACES

Abstract

Let \(\mathbb{D}\) be the unit disk in the complex plane \(\mathbb{C}\) and H(\(\mathbb{D}\)) the class of all analytic functions on \(\mathbb{D}\).  Let φ be an analytic self-map of \(\mathbb{D}\) and u ∈ H(\(\mathbb{D}\)).  By constructing some more effective test functions in area Nevanlinna space, in this paper we characterize the boundedness and compactness of product-type operators DⁿM_uC_φ, DⁿC_φM_u, C_φDⁿM_u, M_uDⁿC_φ, M_uC_φDⁿ and C_φM_uDⁿ from area Nevanlinna spaces to Bloch-Orlicz spaces.