Equivalent Norms And Composition Operators Of Weighted Analytic Lipschitz Spaces

In this dissertation, we mainly deal with the function-theoretic properties of weightedanalytic Lipschitz spaces on the unit disk of the complex plane. Our results are madeup of three parts as follows. In the first part (Chapter 3), we first extend Theorem 1 of[K.M. Dyakonov,Equivalent Norms on Lipschitz-type Spaces of Holomorphic Functions,Acta Math., 1997(178): 143-167] and obtain the characterization of weighted analyticLipschitz functions in terms of p-Garsia modules. Secondly, we characterize them byusing higher derivatives and give the associated characterization in terms of Bergman-Carleson measures. Thirdly, we show the associated exponential decay effect as similar toJohn-Nirenberg's Theorem of BMO spaces. In the second part (Chapter 4), we presentsome integral criteria of weighted analytic Lipschitz functions by using higher derivatives.Finally, in the third part (Chapter 5), the pointwise multipliers and composition operatorsof weighted analytic Lipschitz spaces are studied. Some results on the boundedness,ω-compactness, and compactness of the composition operators on the spaces are obtained.