IMAL   13325
INSTITUTO DE MATEMATICA APLICADA DEL LITORAL "DRA. ELEONOR HARBOURE"
Unidad Ejecutora - UE
artículos
Título:
The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces
Autor/es:
GLADIS PRADOLINI; ESTEFANÍA DALMASSO; WILFREDO RAMOS
Revista:
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
Editorial:
WALTER DE GRUYTER GMBH
Referencias:
Lugar: Berlín; Año: 2018 vol. 21 p. 628 - 653
ISSN:
1311-0454
Resumen:
We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a H"ormander´s type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of $p$.