Integral Criteria for Weighted Bloch Functions

Abstract

The present manuscript gives analytic characterizations and interesting technique that involves the study of general $\varpi$ -Besov classes of analytic functions by the help of analytic $\varpi$ -Bloch functions. Certain special functions significant in both $\varpi$ -Besov-norms and $\varpi$ -Bloch norms framework and to introduce new important families of analytic classes. Interesting motivation of this concerned paper is to construct some new analytic function classes of general $\varpi$ -Besov-type spaces via integrals on concerned functions view points. The introduced analytic $\varpi$ -Bloch and $\varpi$ -Besov type of functions with some interesting properties for these classes of function spaces are established within the constructions of their norms. Using the defined analytic function spaces, various important relations are also derived.