Transferring monotonicity in weighted norm inequalities
- Autores: Gord Sinnamon
- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 54, Fasc. 2, 2003, págs. 181-216
- Idioma: inglés
- Títulos paralelos:
- Transferencia de monotonicidad en desigualdades de norma ponderada
- Enlaces
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Resumen
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.
