Sparse and weighted estimates for generalized Hörmander operators and commutators
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In this paper a pointwise sparse domination for generalized Ho ̈rmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in . Relying upon that sparse domination a number of quantitative estimates are derived. Some of them are improvements and complementary results to those contained in a series of papers due to M. Lorente, J. M. Martell, C. P ́erez, S. Riveros and A. de la Torre [29, 28, 27]. Also the quantitative endpoint estimates in  are extended to iterated commutators. Other results that are obtained in this work are some local exponential decay estimates for generalized Ho ̈rmander operators in the spirit of  and some negative results concerning Coifman-Fefferman estimates for a certain class of kernels satisfying particular generalized Ho ̈rmander conditions.