P-summing Bloch mappings on the complex unit disk

Abstract

This thesis investigates the theory of ff p-summing operators and its extensions in vari ous mathematical and more specifically in the geometry of nonlinear operators settings.Our work is divided on four Chapters: In Chapter One, we present fundamental definitions and theorems concerning the ideal of ff p-summing operators. Chapter Two treats Ideal of (p, σ)-absolutely continuous linear operators, focuses on both linear and Lipschitz ff p summing operators, highlighting relevant domination theorems for each class. In Chapter Three we introduce the ideal of ff p-summing Bloch mappings, a recent development by An tonio Jiménez-Vargas. Finally, Chapter Four is dedicated to Bloch-type versions of classical results, including Pietsch’s domination and factorization theorem and Maurey’s extrapola tion theorem. The results presented contribute to the understanding of operator ideals and their role in functional and nonlinear analysis.