Study of Composition Operators in Certain Functional Spaces

TL;DR

This thesis investigates properties of composition operators in functional spaces, including their boundedness, regularity, and inequalities, while also generalizing multi-function compositions and Peetre's theorem.

Contribution

It introduces new generalizations for the composition of multiple functions and extends Peetre's theorem within the context of functional spaces.

Findings

Established conditions for boundedness and regularity of composition operators.

Generalized composition results for more than two functions.

Provided a broader version of Peetre's theorem.

Abstract

In this thesis we study three problems. The first is the superposition of the operators and their proprities, such as boundedness,continuity,regularity and the inequalities of the norms of the composition of functions in some functional spaces. The second is to generalize some results of the composition of more than two functions, and the third is to give a generalization of Peetre's theorem.