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Generalized weighted composition operators on some spaces of analytic functions
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: علوم ریاضی
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Let be an analytic self-map of D, H(D) the class of all analytic functions on D, u 2 H(D) and m be a nonnegative integer. The generalized weighted composition operator induced by and u, denoted by D;u m is defined by (D;u m f)(z) = u(z)f (m)((z)); f 2 H(D); z 2 D: In this thesis first we consider the boundedness and compactness of the generalized weighted composition operator (D;u m ; m 1) from Bloch-type space into weighted Zygmund space and we give some new equivalence conditions for boundedness and compactness of this operator. Next, we study the essential norm of operator D;u m : B ! H and we give four estimates for the essential norm of this operator. In fourth section, we will find several new characterizations for boundedness, essential norm and compactness of generalized weighted composition operators from Bloch-type space into nth weighted type space (Wn; n 1). Finally, we obtain some equivalence conditions for boundedness, essential norm and compactness of weighted composition operators (uC = D;u 0 ) from Bloch-type space (B; = 1) into nth weighted type space (Wn; n 1)
PARALLEL TITLE PROPER
Parallel Title
Generalized weighted composition operators on some spaces of analytic functions