This dissertation is divided into four parts. In the first chapter, we will discuss bounedness of center maximal operators Mω,υ on homogeneous spaces, whereυ,μis Borel measure on X, satisfying doubling property. we obtain an other proof of theorem in [4]. In the second chapter, we will discuss bounedness of maximal operators in Morrey spaces, and obtain an equivalent relation between maximal operators Mq and M, In the third chapter, we will discuss the boundedness of commutators of Calderón-Zygmund operators with RBMO(μ) on Morrey spaces, which the measureμis non doubling. In the last chapter, we will discuss the boundedness ofθ-type Calderon-Zygmund operator on weighted Herz-type Hardy spaces.
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