Weights for singular integrals with nonstandard kernels

M. S. RIVEROS

Sevilla, España

Congreso; · Harmonic and Geometric Analysis with Applications to Partial and Diferential Equations; 2006

Universidad de Sevilla

 We present general framework, to deal with singular integraloperators and commutators of singular integral operators with BMOfunctions  where Hörmander type conditions associated with Youngfunctions are assumed on the kernels. Coifman type estimates,weighted norm inequalities and two-weight estimates are considered.( See [1] and [2])Recently in a joint work with M. Lorente, J.M. Martell and C. Pérezwe have obtained weighted weak-type estimates for pairs of weights(w, Sw) where w is an arbitrary nonnegative function and S isa maximal operator depending on the smoothness of the kernel, forthese type of operators.  One-sided singular integrals, as thedifferential transform operator, are also under study.Bibliography[1] M. Lorente, M.S. Riveros and A. de la Torre,  Weighted estimatesfor singular integral operators satisfying Hörmander´s conditionsof Young type,  J.  Fourier Anal. Apl. 11 (2005), no. 5, 497--509.[2] M. Lorente, J.M. Martell, M.S. Riveros and A. de laTorre  Weighted norm inequalities for commutators of singularintegral operators satisfying Hörmander´s condition of Young type,  preprint.