Hörmander conditions for vector-valued kernels of singular integrals and their commutators

GALLO, ANDREA L.; IBAÑEZ FIRNKORN, GONZALO HUGO; RIVEROS, MARÍA SILVINA

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahia Blanca; Año: 2019 vol. 60 p. 225 - 245

0041-6932

We study Coifman type estimates and weighted norm inequalities for singular integral operators and their commutators, given by the convolution with a vector-valued kernel. We define a weaker Hörmander type condition associated with Young functions for the vector-valued kernels. With this general framework we obtain as an example the result for the square operator and its commutator given in [M. Lorente, M. S. Riveros, and A. de la Torre, J. Math. Anal. Appl. 336 (2007), no. 1, 577?592].