IMAL   13325
INSTITUTO DE MATEMATICA APLICADA DEL LITORAL "DRA. ELEONOR HARBOURE"
Unidad Ejecutora - UE
artículos
Título:
The rho-variation as an operator between maximal operators and singular integrals
Autor/es:
CRESCIMBENI, R.; MAC¨ªAS, R.; MENARGUEZ, T; TORREA, J. L.; VIVIANI, B.
Revista:
JOURNAL OF EVOLUTION EQUATIONS
Editorial:
BIRKHAUSER VERLAG AG
Referencias:
Año: 2009 vol. 9 p. 81 - 102
ISSN:
1424-3199
Resumen:
Abstract. The ¦Ñ-variation and the oscillation of the heat and Poisson semigroups of the Laplacian and Hermite operators (i.e. and −+|x|2) are proved to be bounded from L p(Rn,w(x)dx) into itself (fromThe ¦Ñ-variation and the oscillation of the heat and Poisson semigroups of the Laplacian and Hermite operators (i.e. and −+|x|2) are proved to be bounded from L p(Rn,w(x)dx) into itself (fromand −+|x|2) are proved to be bounded from L p(Rn,w(x)dx) into itself (from L1(Rn,w(x)dx) into weak-L1(Rn,w(x)dx) in the case p = 1) for 1 ¡Ü p < ¡Þ and w being a weight in the Muckenhoupt¡¯s Ap class. In the case p = ¡Þit is proved that these operators do not map L¡Þ into itself. Even more, they map L¡Þ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.1(Rn,w(x)dx) into weak-L1(Rn,w(x)dx) in the case p = 1) for 1 ¡Ü p < ¡Þ and w being a weight in the Muckenhoupt¡¯s Ap class. In the case p = ¡Þit is proved that these operators do not map L¡Þ into itself. Even more, they map L¡Þ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.Ap class. In the case p = ¡Þit is proved that these operators do not map L¡Þ into itself. Even more, they map L¡Þ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.L¡Þ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.