Revista de la
Unión Matemática Argentina
Hörmander conditions for vector-valued kernels of singular integrals and their commutators
Andrea L. Gallo, Gonzalo H. Ibañez Firnkorn, and María Silvina Riveros
Volume 60, no. 1 (2019), pp. 225–245

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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].