Embeddings of concave functions and duals of Lorentz spaces.

Sinnamon, 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 &lt; q &lt; p &lt; ∞. 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 &lt; ∞ \}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 &lt; q &lt; p &lt; ∞. 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 &lt; ∞ }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 -