AbstractIn 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 {\mathcal{A}^{b,c}} for {b>0} of two parameter families
of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces {B_{\alpha+(c-1)}^{p,q}} for {c>1}.
Local saturation of a positive linear convolution operator
