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

Andrea L. Gallo ^[1] ; Gonzalo H. Ibáñez Firnkorn ^[1] ; María Silvina Riveros ^[1]
1. [1] Universidad Nacional de Córdoba
  
  Universidad Nacional de Córdoba
  
  Argentina
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 1, 2019, págs. 225-245
Idioma: inglés
DOI: 10.33044/revuma.v60n1a14
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Resumen
- 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].