Sharp Norm Estimates for the BergmanOperator From Weighted Mixed-norm Spaces to Weighted Hardy Spaces
Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1257-1284

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we give sharp norm estimates for the Bergman operator acting from weightedmixed-norm spaces to weighted Hardy spaces in the ball, endowed with natural norms.
DOI : 10.4153/CJM-2016-005-6
Mots-clés : 47B38, 32A35, 42B25, 32A37, weighted Hardy space, Bergman operator, sharp norm estimate
Cascante, Carme; Fàbrega, Joan; Ortega, Joaquín M. Sharp Norm Estimates for the BergmanOperator From Weighted Mixed-norm Spaces to Weighted Hardy Spaces. Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1257-1284. doi: 10.4153/CJM-2016-005-6
@article{10_4153_CJM_2016_005_6,
     author = {Cascante, Carme and F\`abrega, Joan and Ortega, Joaqu{\'\i}n M.},
     title = {Sharp {Norm} {Estimates} for the {BergmanOperator} {From} {Weighted} {Mixed-norm} {Spaces} to {Weighted} {Hardy} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {1257--1284},
     year = {2016},
     volume = {68},
     number = {6},
     doi = {10.4153/CJM-2016-005-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-005-6/}
}
TY  - JOUR
AU  - Cascante, Carme
AU  - Fàbrega, Joan
AU  - Ortega, Joaquín M.
TI  - Sharp Norm Estimates for the BergmanOperator From Weighted Mixed-norm Spaces to Weighted Hardy Spaces
JO  - Canadian journal of mathematics
PY  - 2016
SP  - 1257
EP  - 1284
VL  - 68
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-005-6/
DO  - 10.4153/CJM-2016-005-6
ID  - 10_4153_CJM_2016_005_6
ER  - 
%0 Journal Article
%A Cascante, Carme
%A Fàbrega, Joan
%A Ortega, Joaquín M.
%T Sharp Norm Estimates for the BergmanOperator From Weighted Mixed-norm Spaces to Weighted Hardy Spaces
%J Canadian journal of mathematics
%D 2016
%P 1257-1284
%V 68
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-005-6/
%R 10.4153/CJM-2016-005-6
%F 10_4153_CJM_2016_005_6

[1] [1] Ahern, P. and Bruna, J., Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball of Cn. Rev. Mat. Iberoamericana 4(1988), no. 1,123–153. Google Scholar | DOI

[2] [2] Anderson, T. C. and Vagharshakyan, A., A simple proof of the sharp weighted estimate for Calderon-Zygmund operators on homogeneous spaces. J. Geom. Anal. 24(2014), 1276–1297. Google Scholar | DOI

[3] [3] Békollé, D., Inégalités à poids pour le projecteur de Bergman dans la boule unité de Cn. Stud. Math. 71(1981), 305–323. Google Scholar

[4] [4] Benedek, A. and Panzone, R., The space Lt, with mixed norm. Duke Math. J. 28(1961), 301–324. Google Scholar

[5] [5] Buckley, S. M., Estimates for operators on weighted spaces and reverse Jensen inequalities. Trans. Amer. Math. Soc. 340(1993), no. 1. 253–272. Google Scholar | DOI

[6] [6] Cascante, C. and Ortega, J. M., Carleson measures for weighted Hardy-Sobolev spaces. Nagoya Math. J. 186(2007), 29–68. Google Scholar

[7] [7] Cascante, C., Weak trace measures on Hardy-Sobolev spaces. Math. Res. Lett. 20(2013), no. 2, 235–254. Google Scholar | DOI

[8] [8] Christ, M., A T(b) theorem with remarks on analytic capacity and the Cauchy integral. Colloq. Math. 60/61(1990), 601–628. Google Scholar

[9] [9] Cohn, W. S., The Bergman projection and vector-valued Hardy spaces. Michigan Math. J. 44(1997), no. 3, 509–528. Google Scholar | DOI

[10] [10] Coifman, R. R. and Fefferman, C., Weighted norm inequalities for maximal functions and singular integrals. Studia Math. 51(1974), 241–250. Google Scholar

[11] [11] Cruz-Uribe, D., Martell, J.M., and Perez, C., Sharp weighted estimates for classical operators. Adv.Math. 229(2012), no. 1, 408–441. http://dx.doi.Org/10.1016/j.aim.2011.08.013 Google Scholar

[12] [12] Damian, W., Lerner, A. K., and Perez, C., Sharp weighted bounds for multilinear maximal functions and Calderon-Zygmund operators. J. Fourier Anal. Appl. 21(2015), no. 1,161–181. http://dx.doi.Org/10.1007/s00041-014-9364-z Google Scholar

[13] [13] Dragicevic, O., Grafakos, L., Pereyra, M. C., and Petermichl, S., Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces. Publ. Mat. 49(2005), no. 1, 73–91. http://dx.doi.Org/10.5565/PUBLMAT_49105_03 Google Scholar

[14] [14] Duoandikoetxea, J., Fourier analysis. Graduate Studies in Mathematics 29. American Mathematical Society, Providence, RI, 2001. Google Scholar

[15] [15] Duoandikoetxea, J., Extrapolation of weights revisited: new proofs and sharp bounds. J. Funct. Anal. 260(2011),no. 6, 1886–1901. http://dx.doi.Org/10.1016/j.jfa.2010.12.015 Google Scholar

[16] [16] Fefferman, R. and Pipher, J., Multiparameter operators and sharp weighted inequalities. Amer. J. Math. 119(1997), no. 2, 337–369. Google Scholar

[17] [17] Hollenbeck, B. and Verbitsky, I. E., Best constants for the Riesz projection. J. Funct. Anal. 175(2000),370–392. Google Scholar | DOI

[18] [18] Hunt, R., Muckenhoupt, B., and Wheeden, R., Weighted norm inequalities for the conjugate function and Hilbert transform. Trans. Amer. Math. Soc. 176(1973), 227–251. Google Scholar

[19] [19] Hytônen, T. P., The sharp weighted bound for general Calderon-Zygmund operators. Ann. of Math. (2) 175(2012), no. 3, 1473–1506. http://dx.doi.Org/10.4007/annals.2012.175.3.9 Google Scholar

[20] [20] Hytônen, T. P. and Kairema, A., Systems of dyadic cubes in a doubling metric space. Colloq. Math. 126(2012), no. 1, 1–33. Google Scholar | DOI

[21] [21] Jawerth, B. and Torchinsky, A., The strong maximal function with respect to measures. Studia Math. 80(1984), no. 3, 261–285. Google Scholar

[22] [22] Kairema, A., Two-weight norm inequalities for potential type and maximal operators in a metric space. Publ. Mat. 57(2013), no. 1, 3–56. Google Scholar | DOI

[23] [23] Lee, J. and Rim, K. S., Weighted norm inequalities for pluriharmonic conjugate functions. J. Math. Anal. Appl. 268(2002), no. 2, 707–717. Google Scholar | DOI

[24] [24] Lerner, A. K., A pointwise estimate for the local sharp maximal function with applications to singular integrals. Bull. London Math. Soc. 42(2010) no. 5 843–856. http://dx.doi.Org/10.1112/blms/bdqO42 Google Scholar

[25] [25] Lerner, A. K.,Sharp weighted norm inequalities for Littlewood-Paley operators and singular integrals. Adv. Math. 226(2011), no. 5, 3912–3926. http://dx.doi.Org/10.1016/j.aim.2O10.11.00 Google Scholar

[26] [26] Lerner, A. K.,A local mean oscillation decomposition and some of its applications. Function spaces, approximation, inequalities and linearity. Lect. of the Spring School in Anal., Matfyzpress, Prague (2011), 71–106. Google Scholar

[27] [27] Lerner, A. K.,A simple proof of the A conjecture. Int. Math. Res. Not. IMRN (2013), no 14, 3159–3170 Google Scholar

[28] [28] Lerner, A. K.,On sharp aperture-weighted estimates for square functions. J. Fourier Anal. Appl. 20(2014), no 4, 784–800. Google Scholar | DOI

[29] [29] Luecking, D. H., Representation and duality in weighted spaces of analytic functions. Indiana Univ. Math. J. 34(1985), no. 2, 319–336. http://dx.doi.Org/10.1512/iumj.1985.34.34019 Google Scholar

[30] [30] Luque, T., Perez, C., and Rela, E., Optimal exponents in weighted estimates without examples. Math. Res. Lett. 22(2015), no. 1, 183–201. Google Scholar | DOI

[31] [31] Pavlovic, M., On the Littlewood-Paley g-function and Calderôn's area theorem. Expo. Math. 31(2013), no. 2, 169–195. http://dx.doi.Org/10.1016/j.exmath.2O13.01.006 Google Scholar

[32] [32] Pott, S. and Reguera, M. C., Sharp Békollé estimates for the Bergman projection. J. Funct. Anal. 265 (2013), no. 12,3233–3244. http://dx.doi.Org/10.1016/j.jfa.2013.08.018 Google Scholar

[33] [33] Rudin, W., Function theory in the unit ball of ℂn. Grundlehren der Mathematischen Wissenschaften 241, Springer-Verlag, New York, 1980. Google Scholar

[34] [34] Stein, E. M., Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton Mathematical Series 43. Monographs in Harmonic Analysis III, 1993. Google Scholar

[35] [35] Tchoundja, E., Carleson measures for the generalized Bergman spaces via a T(l)-type theorem. Ark. Mat. 46(2008), 377–406. Google Scholar | DOI

[36] [36] Wilson, M., The intrinsic square function. Rev. Mat. Iberoam. 23(2007), no. 3, 771–791. Google Scholar | DOI

Cité par Sources :