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In this article, we consider a two parameter family of generalized Cesáro operators P b,c , Re (b + 1) > Re c > 0, on classical spaces of analytic functions such as Hardy (H p ), BM OA and a-Bloch space (B a ). We Prove that P b,c , Re (b + 1) > Re c > 0 is bounded on H p if and only if p ∈ (0, ∞) and on B a if and only if a ∈ (1, ∞) and unbounded on H ∞ , BM OA and B a , a ∈ (0, 1]. Also we prove that α-Cesáro operators C α is a bounded operator from the Hardy space H p to the Bergmann space A p for p ∈ (0, 1). Thus, we improve some well known results of the literature.

Based on the Borel transformation and the Hadamard multiplication theorem on singularities on the convolution of holomorphic functions, results on the growth of entire functions defined by convolution of an entire function of exponential type with a function holomorphic at the origin are obtained.