Embeddings of concave functions and duals of Lorentz spaces.

Título inglés Embeddings of concave functions and duals of Lorentz spaces.
Título español Inmersiones de funciones cóncavas y duales de espacios de Lorentz.
Autor/es Sinnamon, Gord
Organización Dep. Math. Univ. Western Ontario, London (Ontario), Canadá
Revista 0214-1493
Publicación 2002, 46 (2): 489-515, 18 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés A simple expression is presented that is equivalent to the norm of the Lpv → Lqu embedding of the cone of quasi-concave functions in the case 0 < q < p < ∞. The result is extended to more general cones and the case q = 1 is used to prove a reduction principle which shows that questions of boundedness of operators on these cones may be reduced to the boundedness of related operators on whole spaces. An equivalent norm for the dual of the Lorentz space

Γp(v) = { f: ( ∫0 (f**)pv )1/p < ∞ }

is also given. The expression is simple and concrete. An application is made to describe the weights for which the Hardy Littlewood Maximal Function is bounded on these Lorentz spaces.
Clasificación UNESCO 120206
Palabras clave español Desigualdades ; Espacios de Lorentz ; Espacio dual ; Funciones convexas ; Conos ; Operador maximal de Hardy-Littlewood ; Desigualdad de Hardy
Código MathReviews MR1934367
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