The Hardy Space of Analytic Functions Associated with Certain One-Parameter Families of Integral Operators

Recently, H. M. Srivastava and S. Owa [J. Math. Anal, Appl.118 (1986), 80-87] proved a number of results relevant to Komatu′s conjectures (cf. Y. Komatu [Bull. Fac. Sci. Engrg. Chuo Univ. Ser. I Math.22 (1979), 1-22]) for a certain one-parameter additive family of operators defined on analytic functions regular in the open unit disk. The object of the present paper is to investigate several one-parameter families of integral operators and to prove certain inclusion theorems involving the Hardy space Hp of analytic functions and the class of functions whose derivative has a positive real part. An application involving a generalized hypergeometric function is also considered.