SOME PROPERTIES OF CONVOLUTION-OPERATORS IN THE CLASS P(ALPHA)(BETA)

Making use of several families of convolution operators, we introduce and study a certain general class P(alpha)(beta) (0 less-than-or-equal -to alpha < 1; beta greater-than-or-equal-to 0) of analytic functions in the open unit disk U. We also investigate the relationships between the class P(alpha)(beta) and the Hardy space H(infinity) (of bounded analytic functions in U). Finally, we consider some interesting applic ations of the results presented here to a class of generalized hyperge ometric functions. (C) 1994 Academic Press, Inc.