1,009 research outputs found
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
Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators
In this paper we obtain quite general and definitive forms for
Hardy-Littlewood type inequalities. Moreover, when restricted to the original
particular cases, our approach provides much simpler and straightforward proofs
and we are able to show that in most cases the exponents involved are optimal.
The technique we used is a combination of probabilistic tools and of an
interpolative approach; this former technique is also employed in this paper to
improve the constants for vector-valued Bohnenblust--Hille type inequalities.Comment: 16 page
When is the Haar measure a Pietsch measure for nonlinear mappings?
We show that, as in the linear case, the normalized Haar measure on a compact
topological group is a Pietsch measure for nonlinear summing mappings on
closed translation invariant subspaces of . This answers a question posed
to the authors by J. Diestel. We also show that our result applies to several
well-studied classes of nonlinear summing mappings. In the final section some
problems are proposed
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