# Embeddings of concave functions and duals of Lorentz spaces.

Publicacions Matemàtiques (2002)

- Volume: 46, Issue: 2, page 489-515
- ISSN: 0214-1493

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topSinnamon, Gord. "Embeddings of concave functions and duals of Lorentz spaces.." Publicacions Matemàtiques 46.2 (2002): 489-515. <http://eudml.org/doc/41463>.

@article{Sinnamon2002,

abstract = {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 spaceΓp(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.},

author = {Sinnamon, Gord},

journal = {Publicacions Matemàtiques},

keywords = {Desigualdades; Espacios de Lorentz; Espacio dual; Funciones convexas; Conos; Operador maximal de Hardy-Littlewood; Desigualdad de Hardy},

language = {eng},

number = {2},

pages = {489-515},

title = {Embeddings of concave functions and duals of Lorentz spaces.},

url = {http://eudml.org/doc/41463},

volume = {46},

year = {2002},

}

TY - JOUR

AU - Sinnamon, Gord

TI - Embeddings of concave functions and duals of Lorentz spaces.

JO - Publicacions Matemàtiques

PY - 2002

VL - 46

IS - 2

SP - 489

EP - 515

AB - 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 spaceΓp(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.

LA - eng

KW - Desigualdades; Espacios de Lorentz; Espacio dual; Funciones convexas; Conos; Operador maximal de Hardy-Littlewood; Desigualdad de Hardy

UR - http://eudml.org/doc/41463

ER -

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