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

Transformación morfológica y funcional del borde oriental de Bogotá: explicaciones sobre la gentrificación y la segregación residencial de áreas centrales

El borde oriental de Bogotá ha experimentado transformaciones en su morfología en los últimos 40 años, cuyas consecuencias se relacionan con fenómenos de cambio de uso, segregación, crecimiento en altura, presión sobre la infraestructura, mayor densidad poblacional, elitización y expulsión de habitantes originales. Estas transformaciones responden a factores socio-espaciales particulares. Adicionalmente, en los últimos 15 años la ciudad de Bogotá ha presentado un proceso de densificación en altura resultado del agotamiento del suelo urbanizable. A partir de esta situación, el borde oriental, dada su proximidad al centro histórico y a los centros financieros de la ciudad, se vuelve atractivo para estos desarrollos, transformando su morfología e imagen urbana así como la estructura social de estos sectores.The eastern edge of Bogotá has undergone changes in their morphology in the past 40 years, the consequences are related phenomena use change, segregation, height growth, pressure on infrastructure, increased population density, gentrification and expulsion of original inhabitants. These changes respond to particular socio-spatial factors. Additionally, in the last 15 years Bogotá has introduced a process of densification in height result of the exhaustion of land for development. From this, the eastern edge, given its proximity to the historic center and the financial centers of the city, becomes attractive to these developments, transforming their morphology and urban image and social structure of these sectors

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