Sparse and weighted estimates for generalized Hörmander operators and commutators
Abstract
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 [24]. 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 [24] 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 [33] and some negative results concerning Coifman-Fefferman estimates for a certain class of kernels satisfying particular generalized Ho ̈rmander conditions.