Characterizations of weight classes for multilinear integral operators and sparse forms

• Diego Maldonado ^[1]
  1. [1] Kansas State University

     Kansas State University

     City of Manhattan, Estados Unidos

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 319-335
• Idioma: inglés
• DOI: 10.33044/revuma.5648
• Enlaces
  • Texto completo
• Resumen

  • The class of Muckenhoupt weights has been extended to the multilinear setting in several contexts of real and Fourier analysis. In this work, we provide new characterizations of these multilinear weight classes through a unifying principle based on pointwise, rather than averaged, evaluation of the weights.

• Referencias bibliográficas
  • F. Bernicot, D. Maldonado, K. Moen, and V. Naibo, Bilinear Sobolev–Poincaré inequalities and Leibniz-type rules, J. Geom. Anal. 24 no. 2 (2014),...
  • T. A. Bui and X. T. Duong, Weighted norm inequalities for multilinear operators and applications to multilinear Fourier multipliers, Bull....
  • S. Chen, H. Wu, and Q. Xue, A note on multilinear Muckenhoupt classes for multiple weights, Studia Math. 223 no. 1 (2014), 1–18. DOI MR...
  • X. Chen and Q. Xue, Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl. 362 no. 2 (2010), 355–373....
  • R. R. Coifman and Y. Meyer, On commutators of singular integrals and bilinear singular integrals, Trans. Amer. Math. Soc. 212 (1975), 315–331....
  • R. R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque 57, Société Mathématique de France, Paris, 1978. MR ...
  • R. R. Coifman and Y. Meyer, Commutateurs d'intégrales singulières et opérateurs multilinéaires, Ann. Inst. Fourier (Grenoble) 28 no. 3...
  • D. Cruz-Uribe and K. Moen, A multilinear reverse Hölder inequality with applications to multilinear weighted norm inequalities, Georgian Math....
  • W. Damián, A. K. Lerner, and C. Pérez, Sharp weighted bounds for multilinear maximal functions and Calderón–Zygmund operators, J. Fourier...
  • L. Grafakos, Modern Fourier analysis, second ed., Grad. Texts in Math. 250, Springer, New York, 2009. DOI MR Zbl
  • L. Grafakos, P. Mohanty, and S. Shrivastava, Multilinear square functions and multiple weights, Math. Scand. 124 no. 1 (2019), 149–160. DOI...
  • L. Grafakos and R. H. Torres, Maximal operator and weighted norm inequalities for multilinear singular integrals, Indiana Univ. Math. J. 51...
  • K. Li, J. M. Martell, and S. Ombrosi, Extrapolation for multilinear Muckenhoupt classes and applications, Adv. Math. 373 (2020), Paper no....
  • K. Li, K. Moen, and W. Sun, The sharp weighted bound for multilinear maximal functions and Calderón–Zygmund operators, J. Fourier Anal. Appl....
  • K. Li, K. Moen, and W. Sun, Sharp weighted inequalities for multilinear fractional maximal operators and fractional integrals, Math. Nachr....
  • K. Li and W. Sun, Weighted estimates for multilinear Fourier multipliers, Forum Math. 27 no. 2 (2015), 1101–1116. DOI MR Zbl
  • D. Maldonado, A Harnack-type characterization of A-weights and applications, Canad. Math. Bull. (2026). DOI
  • K. Moen, Weighted inequalities for multilinear fractional integral operators, Collect. Math. 60 no. 2 (2009), 213–238. DOI MR Zbl
  • L. Grafakos and R. H. Torres, Multilinear Calderón–Zygmund theory, Adv. Math. 165 no. 1 (2002), 124–164. DOI MR Zbl
  • T. Hytönen and S. Lappas, Extrapolation of compactness on weighted spaces: Bilinear operators, Indag. Math. (N.S.) 33 no. 2 (2022), 397–420....
  • C. E. Kenig and E. M. Stein, Multilinear estimates and fractional integration, Math. Res. Lett. 6 no. 1 (1999), 1–15. Erratum: ibid. 6 no....
  • M. Lacey and C. Thiele, On Calderón's conjecture, Ann. of Math. (2) 149 no. 2 (1999), 475–496. DOI MR Zbl
  • A. K. Lerner, S. Ombrosi, C. Pérez, R. H. Torres, and R. Trujillo-González, New maximal functions and multiple weights for the multilinear...
  • M. Lacey and C. Thiele, Lp estimates on the bilinear Hilbert transform for 2 p∞, Ann. of Math. (2) 146 no. 3 (1997), 693–724. DOI MR Zbl