Transferring monotonicity in weighted norm inequalities.

Título inglés	Transferring monotonicity in weighted norm inequalities.
Título español	Transferencia de monotonicidad en desigualdades de norma ponderada.
Autor/es	Sinnamon, Gord
Organización	Dep. Math. Univ. Western Ontario, London (Ontario), Canadá
Revista	0010-0757
Publicación	2003, 54 (2): 181-216, Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	Certain weighted norm inequalities for integral operators with non-negative, monotone kernels are shown to remain valid when the weight is replaced by a monotone majorant or minorant of the original weight. A similar result holds for operators with quasi-concave kernels. To prove these results a careful investigation of the functional properties of the monotone envelopes of a non-negative function is carried-out. Applications are made to function space embeddings of the cones of monotone functions and quasi-concave functions. Under weaker partial orders on non-negative functions, monotone envelopes are re-examined and the level function is recognized as a monotone envelope in two ways. Using the level function, monotonicity can be transferred from the kernel to the weight in inequalities restricted to a cone of monotone functions.
Clasificación UNESCO	120206
Palabras clave español	Desigualdades ; Espacios de funciones medibles ; Monotonicidad ; Funciones de peso
Código MathReviews	MR1995140
Código Z-Math	Zbl 1093.26025
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