CIEM   05476
CENTRO DE INVESTIGACION Y ESTUDIOS DE MATEMATICA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Weights for singular integrals with nonstandard kernels
Autor/es:
M.S. RIVEROS
Lugar:
Madrid, España
Reunión:
Congreso; International Congress of Mathematicians (ICM2006),; 2006
Institución organizadora:
IMU
Resumen:
This is a joint work with M. Lorente, J.M. Martell and C. Pérez. In [1] and [ 2] it was considered a general framework to deal with singular integral operators and commutators of singular integral operators with BMO functions where Hörmander type conditions associated with Young functions are assumed on the kernels. More precisely, the kernels are those that satisfy the following definition
Definition:Let Ke L1 loc( Rn-{ 0}), and let A be a Young function. We say that the kernel Ksatisfies the L A$-Hörmander condition if there are positive numbers cA geq1 and C Asuch that for any x and R>cA |x|,
(H A) sum m=1 (2mR)n||K(x-.)-K(-.)cS m,R(.)|| A,B m,R leq CA
We say that a kernel K satisfies the Linfty-Hörmander condition if there exist C and cgeq 1, such that, for any x and R>c|x|,
(Hinfty) sum m=1 (2mR)nsup{2mRleq |y|<2m+1R} |K(x-y)-K(-y)|leq C.
In these cited articles are obtained Coifman type estimates, weighted norm inequalities and two-weight estimates. In the present work we give weighted weak-type estimates for pairs of weights (w, Sw) where w is an arbitrary nonnegative function
and S is a maximal operator depending on the smoothness of the kernel. One-sided singular integrals, as the differential transform operator, are under study. We also provide applications to Fourier multipliers and homogeneous singular integrals.
Bibliography
[1] M. Lorente, M.S. Riveros and A. de la Torre, Weighted estimates
for singular integral operators satisfying Hörmander's conditions
of Young type, J. Fourier Anal. Apl. 11 (2005), no. 5, 497--509.
[2] M. Lorente, J.M. Martell, M.S. Riveros and A. de la
Torre, Weighted norm inequalities for commutators of singular
integral operators satisfying Hömander's condition of Young type,
preprint.