Characterizations Of The Bloch Type Spaces With The Ces(?)ro Means

In this thesis, using the Ces(?)ro means of Taylor expansions of holomorphic functions on the unit disc, the theoretical properties of some function spaces are studied. The thesis consists of the following parts.In the first chapter, we recite the investigative current circumstance of function spaces with the Cesaro means, and some known conclusions in terms of the Ces(?)ro means are given.In the second chapter, the Q_K(p,q) spaces are studied by using the Cesaro means. Our first result is the following:sup{||σ_n(f)||Q_K(p,q) : n ∈ N U {0}} = ||f||Q_K(p,q).We consider the α-Bloch spaces B^α via the Cesaro means in the last chapter. In order to prove our main result, a theorem in [1] is need to be extended. Main Theorem(i) f ∈ B^α, 0<α< 3/2;(ii) ||(n + m + 1)σ_n+m(f) - (n + 1)σ_n(f) - (m + 1)σ_m(f)||_∞= O((nm)^1/2(n^α/2-1/2m^<sup>α/2-1/2+ n^α-1 + mn^α-1)), n,m → ∞;(iii) ||σ_2n(f)-σ_n(f)||_∞=O(n^α-1).