Some techniques on nonlinear analysis and applications

TL;DR

This paper introduces a versatile nonlinear analysis technique applicable to various problems and extends the Pietsch Domination Theorem to unify previous results and explore connections to weighted summability.

Contribution

It presents a new general nonlinear technique and a comprehensive extension of the Pietsch Domination Theorem unifying earlier versions and clarifying their scope.

Findings

A new nonlinear technique with broad applicability.

The 'full general Pietsch Domination Theorem' unifies previous versions.

Connections established between domination results and weighted summability.

Abstract

In this paper we present two different results in the context of nonlinear analysis. The first one is essentially a nonlinear technique that, in view of its strong generality, may be useful in different practical problems. The second result, more technical, but also connected to the first one, is an extension of the well-known Pietsch Domination Theorem. The last decade witnessed the birth of different families of Pietsch Domination-type results and some attempts of unification. Our result, that we call "full general Pietsch Domination Theorem" is potentially a definitive Pietsch Domination Theorem which unifies the previous versions and delimits what can be proved in this line.The connections to the recent notion of weighted summability are traced.