This is an announcement for the paper "A generalized unified Pietsch domination theorem and applications" by Daniel Pellegrino and Joedson Santos.

Abstract: This paper has a twofold purpose. Firstly, we provide a new version of the Pietsch Domination Theorem that contains all the previous versions (to the best of our knowledge) as particular cases; our second goal is to characterize the arbitrary nonlinear mappings $f:X_{1}\times\cdots\times X_{n}\rightarrow Y$ that satisfy a quite natural Pietsch Domination-type theorem around a given point $(a_{1},...,a_{n})\in$ $X_{1}\times\cdots\times X_{n};$ as it will be shown, the new Pietsch Domination-type theorem plays a crucial role in this task. The characterization of such mappings lead to the idea of a kind of weighted summability for arbitrary mappings.

Archive classification: math.FA

Remarks: 12 pages

Submitted from: dmpellegrino@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1004.2643

or

http://arXiv.org/abs/1004.2643