Adjoint of generalized Cesáro operators on analytic function spaces

Abstract

Abstract In this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular, we obtain a well-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 2009, 2, 304–311]. Also we consider the adjoint 𝒜 b , c {\mathcal{A}^{b,c}} for b > 0 {b>0} of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces B α + ( c - 1 ) p , q {B_{\alpha+(c-1)}^{p,q}} for c > 1 {c>1} .