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Sparse and weighted estimates for generalized Hörmander operators and commutators

  • Gonzalo H. Ibañez-Firnkorn
  • Israel P. Rivera-RíosEmail author
Article
  • 13 Downloads

Abstract

In this paper a pointwise sparse domination for generalized Hörmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in Lerner et al. (Adv Math 319:153–181, 2017). 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 Lorente et al. (Stud Math 195(2):157–192, 2009, J Math Anal Appl 342(2):1399–1425, 2008, J Fourier Anal Appl 11(5):497–509, 2005). Also the quantitative endpoint estimates in Lerner et al. (Adv Math 319:153–181, 2017) are extended to iterated commutators. Other results that are obtained in this work are some local exponential decay estimates for generalized Hörmander operators in the spirit of Ortiz-Caraballo et al. (Math Ann 357(4):1217–1243, 2013) and some negative results concerning Coifman–Fefferman estimates for a certain class of kernels satisfying particular generalized Hörmander conditions.

Keywords

Commutators Generalized Hörmander conditions Sparse operators Weighted inequalities Calderón–Zygmund operators 

Mathematics Subject Classification

42B20 42B25 

Notes

Acknowledgements

The first author would like Carlos Pérez for inviting him to visit BCAM between January and April 2017, and BCAM for the warm hospitality shown during his visit.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.BCAM - Basque Center for Applied MathematicsBilboSpain
  2. 2.FaMAFUniversidad Nacional de CórdobaCórdobaArgentina
  3. 3.CIEM-CONICETCórdobaArgentina
  4. 4.Departamento de Matemáticas/Matematika SailaUniversidad del País Vasco/Euskal Herriko UnibertsitateaLeioaSpain
  5. 5.Departamento de MatemáticaUniversidad Nacional del SurBahía BlancaArgentina
  6. 6.INMABB-CONICETBahía BlancaArgentina

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