Boundedness of generalized Cesàro averaging operators on certain function spaces
Given an infinite matrix \(A\) with complex entries, we can consider the transformation that takes an analytic function in the unit disk \(D\), \(f(z)=\sum_{n=0}^\infty a_n z^n\) into the function \(g(z)= \sum_{n=0}^\infty b_n z^n\), where \(b=Aa\) and the problem of study for which function spaces \(\mathcal F\) of analytic functions in \(D\), this operator is bounded in general, a quite hard problem. In this paper the authors deal with a particular case of a matrix \(A\) whose coefficients appear related to the classical hypergeometric function. They first prove an integral representation for this operator and then study the boundedness of it in spaces of the type Hardy, BMOA and Bloch.
scientific article; zbMATH DE number 2175282
scientific article