Generalized multiplication operators on weighted hardy spaces

Abstract

The main purpose of this paper is to study generalized multiplication operators on weighted hardy spaces.

On weighted generalized composition operators on weighted hardy spaces

“…The tendency of these operators to induce new classes of operators and their wide appearance have motivated mathematicians to come up with various generalizations of these operators. In the recent times, the generalized multiplication operators on weighted Hardy spaces have been introduced in [12] and further extended to k th -order generalized multiplication operators in [5], where k ≥ 1 is an integer. In a parallel manner, the study of generalized composition operators of higher order on weighted Hardy spaces H 2 (β) has been undertaken (see [4] and the references therein).…”

Fredholm generalized composition operators on weighted hardy spaces

“…Composition operators on the spaces of analytic functions were studied by Cowen [1], Ryff [4], Schwartz [5]and Singh [8]. Properties of generalized composition operators on weighted Hardy spaces were mentioned in the papers of Sharma [6]- [7], further Fredholm composition and weighted composition operators can be seen in the papers of Kumar [2], Maccluer [3] and Takagi [9]. In this paper we initiate the study of Fredholm generalized composition operators on weighted Hardy spaces.…”

Adjoint of generalized weighted composition operators using evaluation kernel on weighted Hardy space

“…where f denotes the derivative of function f . For θ(z) = 1 the generalized weighted composition operator becomes generalized composition operators and for φ(z) = z generalized weighted composition operator becomes well known generalized multiplication operators which was studied in [3]- [4]. Further weighted composition operators is also the part of generalized weighted composition operators.…”