Sparse and weighted estimates for generalized Hörmander operators and commutators

IBAÑEZ-FIRNKORN, GONZALO H.; RIVERA-RÍOS, ISRAEL P.

MONATSHEFETE FUR MATHEMATIK

SPRINGER WIEN

Año: 2019

0026-9255

In this paper a pointwise sparse domination for generalized Hörmanderand also for iterated commutators with those operators is providedgeneralizing the sparse domination result in [LORR]. Relyingupon that sparse domination a number of quantitative estimates arederived. Some of them are improvements and complementary results tothose contained in a series of papers due to M. Lorente, J. M. Martell,C. Pérez, S. Riveros and A. de la Torre [LoRiTo,LoMaRiTo,LoMaPeRi].Also the quantitative endpoint estimates in [LORR] are extendedto iterated commutators. Other results that are obtained in this workare some local exponential decay estimates for generalized Hörmanderoperators in the spirit of [OCPR] and some negative resultsconcerning Coifman-Fefferman estimates for a certain class of kernelssatisfying particular generalized Hörmander conditions.