Real interpolation methods and Sobolev and Besov espaces on the Sd sphere / Metodos de interpolação real e espaços de Sobolev e Besov sobre a esfera Sd

AUTOR(ES)

Andrielber da Silva Oliveira

DATA DE PUBLICAÇÃO

2006

RESUMO

The purpose of this work is to make a study about Besov?s spaces on the unit d-dimensional real sphere Sd. In the first chapter are studied spaces of interpolation using two real interpolation methods. In particular, are studied The Equivalence Theorem and The Reiteration Theorem for the J-method and the K-method. In the second chapter it is made a short study about harmonic analysis on the sphere Sd, including a study about spherics harmonics, zonal harmonics, Cesàro sums and about a multiplier theorem. The third and last chapter is the most important of this work. In this chapter are applied the results of the others chapters. Are introduced the Besov spaces, decomposing a smooth function defined on the d-dimensional sphere, in a series of harmonics spherics and using a sequence o zonal polynomials which can be seen as a natural generalization of the Vallée Poussin polynomials defined on the unit circle. The main result studied says that every Besov?s space can be got as a interpolation space of two Sobolev?s spaces

ASSUNTO(S)

sobolev interpolation spaces analise harmonica analise funcional espaços de interpolação functional analysis harmonic analysis sobolev spaces espaços de

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