Optimal Sobolev embeddings on Rn.

Título inglés Optimal Sobolev embeddings on Rn.
Título español Inmersiones de Sobolev óptimas en Rn.
Autor/es Vybíral, Jan
Organización Dep. Math. Anal. Fac. Math. Phys. Charles Univ., Praga, Rep. Checa;Math. Inst. Friedrich-Schiller-Univ. Jena, Jena, Alemania
Revista 0214-1493
Publicación 2007, 51 (1): 17-44, 14 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés We study Sobolev-type embeddings involving rearrangement-invariant norms. In particular, we focus on the question when such embeddings are optimal. We concentrate on the case when the functions involved are defined on Rn. This subject has been studied before, but only on bounded domains. We first establish the equivalence of the Sobolev embedding to a new type of inequality involving two integral operators. Next, we show this inequality to be equivalent to the boundedness of a certain Hardy operator on a specific new type of cone of positive functions. This Hardy operator is then used to provide optimal domain and range rearrangement-invariant norm in the embedding inequality. Finally, the limiting case of the Sobolev embedding on Rn is studied in detail.
Clasificación UNESCO 120200
Palabras clave español Espacios de funciones lineales ; Espacios de funciones medibles ; Espacios de Sobolev ; Inmersiones
Código MathReviews MR2307145
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