Refined two weight estimates for the Bergman projection

• Brocchi, Gianmarco ^[1]
  1. [1] University of Birmingham

     University of Birmingham

     Reino Unido

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 76, Fasc. 1, 2025, págs. 65-80
• Idioma: inglés
• DOI: 10.1007/s13348-023-00420-w
• Texto completo no disponible (Saber más ...)
• Resumen

  • We prove sufficient conditions for the two-weight boundedness of the Bergman projection on the unit ball. The first condition is in terms of Orlicz averages of the weights, while the second condition is in terms of the mixed B_{\infty } - B_2 characteristics.

• Referencias bibliográficas
  • Anderson, T.C.: A new sufficient two-weighted bump assumption for Lp boundedness of Calderón–Zygmund operators. Proc. Am. Math. Soc. 143(8),...
  • Aleman, A., Pott, S., Reguera, M.C.: Sarason conjecture on the Bergman space. Int. Math. Res. Not. IMRN 14, 4320–4349 (2017)
  • Aleman, A., Pott, S., Reguera, M.C.: Characterizations of a limiting class B∞ of Békollé–Bonami weights. Rev. Mat. Iberoam. 35(6), 1677–1692...
  • Arcozzi, N., Rochberg, R., Sawyer, E.: Carleson measures for analytic Besov spaces. Rev. Mat. Iberoam. 18(2), 443–510 (2002)
  • Arcozzi, N., Rochberg, R., Sawyer, E.: Carleson measures and interpolating sequences for Besov spaces on complex balls. Mem. Am. Math. Soc....
  • Bekolle, D., Bonami, A.: Inégalités à poids pour le noyau de Bergman. C. R. Acad. Sci. Paris Sér. A 286, 775–778 (1978)
  • Bekollé, D.: Inégalités à poids pour le projecteur de Bergman dans la boule unité de Cn. Stud. Math. 71, 305–323 (1982)
  • Buckley, S.M.: Estimates for operator norms on weighted spaces and reverse Jensen inequalities. Trans. Am. Math. Soc. 340(1), 253–272 (1993)
  • Cruz-Uribe, D., Martell, J.M., Pérez, C.: Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform...
  • Duoandikoetxea, J., Martín-Reyes, F.J., Ombrosi, S.: On the A conditions for general bases. Math. Z. 282(3–4), 955–972 (2016)
  • Dragičević, O., Grafakos, L., Pereyra, M.C., Petermichl, S.: Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue...
  • Forelli, F., Rudin, W.: Projections on spaces of holomorphic functions in balls. Indiana Univ. Math. J. 24, 593–602 (1974)
  • Fang, X., Wang, Z.: Two weight inequalities for the Bergman projection with doubling measures. Taiwan. J. Math. 19(3), 919–926 (2015)
  • Gan, C., Hu, B., Khan, I.: Dyadic decomposition of convex domains of finite type and applications. Math. Z. 301(2), 1939–1962 (2022).
  • Hytönen, T., Kairema, A.: Systems of dyadic cubes in a doubling metric space. Colloq. Math. 126(1), 1–33 (2012)
  • Hytönen, T.P., Lacey, M.T.: The Ap-A inequality for general Calderón-Zygmund operators. Indiana Univ. Math. J. 61(6), 2041–2092 (2012)
  • Hytönen, T., Pérez, C.: Sharp weighted bounds involving A. Anal. PDE 6(4), 777–818 (2013)
  • Huo, Z., Wick, B.D.: Weighted estimates for the Bergman projection on the Hartogs triangle. J. Funct. Anal. 279(9), 108727, 34 (2020)
  • Huo, Z., Wagner, N.A., Wick, B.D.: Bekollé-Bonami estimates on some pseudoconvex domains. Bull. Sci. Math. 170, 102993 (2021)
  • Hytönen, T.P.: The sharp weighted bound for general Calderón–Zygmund operators. Ann. Math. (2) 175(3), 1473–1506 (2012)
  • Hytönen, T.P.: The A2 theorem: remarks and complements. In: Harmonic Analysis and Partial Differential Equations, vol. 612. Contemporary Mathematics...
  • Kosz, D.: A condition for general bases revisited: complete classification of definitions. Proc. Am. Math. Soc. 150(9), 3831–3839 (2022)
  • Lerner, A.K.: An elementary approach to several results on the Hardy–Littlewood maximal operator. Proc. Am. Math. Soc. 136(8), 2829–2833 (2008)
  • Lerner, A.K.: On an estimate of Calderón–Zygmund operators by dyadic positive operators. J. Anal. Math. 121, 141–161 (2013)
  • Li, K.: Two weight inequalities for bilinear forms. Collect. Math. 68(1), 129–144 (2017)
  • Lacey, M.T., Sawyer, E.T., Uriarte-Tuero, I.: Two weight inequalities for discrete positive operators (2009). arXiv:0911.3437 [math.CA]
  • McNeal, J.D.: The Bergman projection as a singular integral operator. J. Geom. Anal. 4(1), 91–103 (1994)
  • Pérez, C.: On sufficient conditions for the boundedness of the Hardy–Littlewood maximal operator between weighted Lp-spaces with different...
  • Pott, S., Reguera, M.C.: Sharp Békollé estimates for the Bergman projection. J. Funct. Anal. 265(12), 3233–3244 (2013)
  • Rahm, R., Tchoundja, E., Wick, B.D.: Weighted estimates for the Berezin transform and Bergman projection on the unit ball. Math. Z. 286(3–4),...
  • Sawyer, E.T.: A characterization of a two-weight norm inequality for maximal operators. Stud. Math. 75(1), 1–11 (1982)
  • Sawyer, E.T.: A characterization of two weight norm inequalities for fractional and Poisson integrals. Trans. Am. Math. Soc. 308(2), 533–545...
  • Sehba, B.F.: Weighted boundedness of maximal functions and fractional Bergman operators. J. Geom. Anal. 28(2), 1635–1664 (2018)
  • Sehba, B.F.: Sawyer-type characterizations and sharp weighted norm estimates for Bergman type operators. Positivity 25(1), 49–71 (2021)
  • Wilson, M.: Weighted Littlewood–Paley Theory and Exponential-Square Integrability. Lecture Notes in Mathematics, vol. 1924, p. xiv+224....
  • Wilson, J.M.: Weighted inequalities for the dyadic square function without dyadic A ∞. Duke Math. J. 55, 19–49 (1987)
  • Zaharjuta, V.P., Judovič, V.I.: The general form of a linear functional in H’p. Usp. Mat. Nauk. 19(2), 139–142 (1964)