Absolutely summing multilinear operators: a panorama

This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective search of \textquotedblleft perfect\textquotedblright \ multilinear extensions of the ideal of absolutely summing operators. The final section contains some open problems that may indicate lines for future investigation.Comment: 30 page

Some techniques on nonlinear analysis and applications

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.Comment: 24 page

A general Extraplolation Theorem for absolutely summing operators

In this note we prove a general version of the Extrapolation Theorem, extending the classical linear extrapolation theorem due to B. Maurey. Our result shows, in particular, that the operators involved do not need to be linear