Theory of Bergman Spaces in the Unit Ball of n  [ Théorie des espaces de Bergman dans la boule unité de n  ] (2008)


Zhao, Ruhan; Zhu, Kehe
Mémoires de la Société Mathématique de France, Tome 115 (2008) vi-103 p
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consulter l'article sur le site de la revue
doi : 10.24033/msmf.427
URL stable : http://www.numdam.org/item?id=MSMF_2008_2_115__1_0

Bibliographie

[1] P. Ahern & W. Cohn« Besov spaces, Sobolev spaces and Cauchy integrals », Michigan Math. J. 39 (1972), p. 239–261. Zbl 0767.46022 | MR 1162034

[2] A. AleksandrovFunction theory in the unit ball, Several Complex Variables II, G.M. Khenkin and A.G. Vitushkin, ed., Springer, 1994.

[3] J. Anderson, J. Clunie & C. Pommerenke« On Bloch functions and normal functions », J. reine angew. Math. 270, p. 12–37. Zbl 0292.30030 | | MR 361090

[4] J. Arazy, S. Fisher, S. Janson & J. Peetre« Membership of Hankel operators on the ball in unitary ideals », J. London Math. Soc. 43 (1991), p. 485–508. Zbl 0747.47019 | MR 1113389

[5] N. Arcozzi« Carleson measures for analytic Besov spaces: the upper triangle case »,, J. Inequal. Pure Appl. Math., 6 (2005) no. 1, Art. 13. Zbl 1127.30313 | | MR 2122940

[6] N. Arcozzi, R. Rochberg & E. Sawyer« Carleson measures for analytic Besov spaces », Rev. Mat. Iberoamericana 18 (2002), p. 443–510. Zbl 1059.30051 | | MR 1949836

[7] —, Carleson measures and interpolating sequences for Besov spaces on complex balls, Memoirs Amer. Math. Soc., vol. 859, 2006. Zbl 1112.46027

[8] W. Arveson« Subalgebras of C * -algebras III, multivariable operator theory », Acta Math. 181 (1998), p. 159–228. Zbl 0952.46035 | MR 1668582

[9] F. Beatrous« Estimates for derivatives of holomorphic functions in pseudoconvex domains », Math. Z. 191 (1986), p. 91–116. Zbl 0596.32005 | | MR 812605

[10] F. Beatrous & J. Burbea« Characterizations of spaces of holomorphic functions in the ball », Kodai Math. J. 8 (1985), p. 36–51. Zbl 0571.32005 | MR 776705

[11] —, Holomorphic Sobolev spaces on the ball, Dissertationes Math., Warszawa, vol. 276, 1989.

[12] J. Bennet, D. Stegenga & R. Timoney« Coefficients of Bloch and Lipschitz functions », Illinois J. Math. 25 (1981), p. 520–531. Zbl 0443.30041 | MR 620437

[13] C. Bennett & R. SharpleyInterpolation of Operators, Academic Press, New York, 1988. Zbl 0647.46057 | MR 928802

[14] J. Bergh & J. LöfströmInterpolation Spaces: An Introduction, Grundlehrem, vol. 223, Springer, Berlin, 1976. Zbl 0344.46071 | MR 482275

[15] L. Carleson« An interpolation problem for bounded analytic functions », Amer. J. Math. 80 (1958), p. 921–930. Zbl 0085.06504 | MR 117349

[16] —, « Interpolation by analytic functions and the corona problem », Ann. Math. 76 (1962), p. 547–559. Zbl 0112.29702

[17] X. Chen & K. GuoAnalytic Hilbert Modules, Chapman Hall/CRC Press, Boca Raton, 2003. MR 1988884

[18] B. R. Choe« Projections, the weighted Bergman spaces and the Bloch space », Proc. Amer. Math. Soc. 108 (1990), p. 127–136. Zbl 0684.47022 | MR 991692

[19] B. R. Choe, H. Koo & H. Yi« Positive Toeplitz operators between harmonic Bergman spaces », Potential Anal. 17 (2002), p. 307–335. Zbl 1014.47014 | MR 1918239

[20] J. Cima & W. Wogen« A Carleson measure theorem for the Bergman space of the ball », J. Operator Theory 7 (1982), p. 157–165. Zbl 0499.42011 | MR 650200

[21] R. Coifman & R. Rochberg« Representation theorems for holomorphic and harmonic functions », Astérisque 77 (1980), p. 11–66. Zbl 0472.46040 | MR 604369

[22] R. Coifman, R. Rochberg & G. Weiss« Factorization theorems for Hardy spaces of several complex variables », Ann. Math. 103 (1976), p. 611–635. Zbl 0326.32011 | MR 412721

[23] P. DurenTheory of H p Spaces, Academic Press, New York, 1970. MR 268655

[24] P. Duren, B. Romberg & A. Shields« Linear functionals on H p spaces with 0<p<1 », J. reine angew. Math. 238 (1969), p. 32–60. Zbl 0176.43102 | | MR 259579

[25] F. Forelli & W. Rudin« Projections on spaces of holomorphic functions on balls », Indiana Univ. Math. J. 24 (1974), p. 593–602. Zbl 0297.47041 | MR 357866

[26] M. Frazier & B. Jawerth« Decomposition of Besov spaces », Indiana Univ. Math. J. 34 (1985), p. 777–799. Zbl 0551.46018 | MR 808825

[27] J. GarnettBounded Analytic Functions, Academic Press, New York, 1981. Zbl 0469.30024 | MR 628971

[28] I. Graham« The radial derivative, fractional integrals and the comparative growth of means of holomorphic functions on the unit ball in n », in Recent Developments in Several Complex Variables, vol. 100, Ann. Math. Studies, 1981, p. 171–178. MR 627757

[29] K. T. Hahn & E. H. Youssfi« M-harmonic Besov spaces and Hankel operators on the Bergman space on ball of n », Manuscripta Math. 71 (1991), p. 67–81. Zbl 0816.31004 | | MR 1094739

[30] —, « Möbius invariant Besov spaces and Hankel operators on the Bergman spaces on the unit ball », Complex Variables 17 (1991), p. 89–104. Zbl 0706.47017

[31] W. Hastings« A Carleson measure theorem for Bergman spaces », Proc. Amer. Math. Soc. 52 (1975), p. 237–241. Zbl 0296.31009 | MR 374886

[32] L. Hörmander« L p estimates for (pluri-)subharmonic functions », Math. Scand. 20 (1967), p. 65–78. Zbl 0156.12201 | | MR 234002

[33] T. Kaptanoglu« Besov spaces and Bergman projections on the ball », C.R. Acad. Sci. Paris, Sér. I 335 (2002), p. 729–732. Zbl 1029.32002 | MR 1951806

[34] —, « Bergman projections on Besov spaces on balls », Illinois J. Math. 49 (2005), p. 385–403. Zbl 1079.32004 | MR 2163941

[35] —, « Carleson measures for Besov spaces on the ball », J. Funct. Anal. 250 (2007), p. 483–520. Zbl 1135.46014 | MR 2352489

[36] O. Kures & K. Zhu« A class of integral operators on the unit ball of n », Integr. Equ. Oper. Theory 56 (2006), p. 71–82. Zbl 1109.47041 | MR 2256998

[37] S. Li, H. Wulan, R. Zhao & K. Zhu« A characterization of Bergman spaces on the unit ball of n », 2007, to appear in Glasgow Math J.

[38] D. Luecking« A technique for characterizing Carleson measures on Bergman spaces », Proc. Amer. Math. Soc. 87 (1983), p. 656–660. Zbl 0521.32005 | MR 687635

[39] —, « Embedding theorems for spaces of analytic functions via Khinchine’s inequality », Michigan Math. J. 40 (1993), p. 333–358. Zbl 0801.46019 | MR 1226835

[40] M. Nowark« Bloch and Möbius invariant Besov spaces on the unit ball of n », Complex Variables 44 (2001), p. 1–12. MR 1826712

[41] C. Ouyang, W. Yang & R. Zhao« Characterizations of Bergman spaces and the Bloch space in the unit ball of n », Trans. Amer. Math. Soc. 374 (1995), p. 4301–4312. Zbl 0849.32005 | MR 1311908

[42] M. Pavlovic« Inequalities for the gradient of eigenfunctions of the invariant Laplacian in the unit ball », Indag. Math. 2 (1991), p. 89–98. Zbl 0731.32003 | MR 1104834

[43] M. Pavlovic & K. Zhu« New characterizations of Bergman spaces », Ann. Acad. Sci. Fen. 33 (2008), p. 87–99. Zbl 1147.32008 | | MR 2386839

[44] M. Peloso« Möbius invariant spaces on the unit ball », Michigan Math. J. 39 (1992), p. 509–536. Zbl 0779.32012 | MR 1182505

[45] S. Power« Hörmander’s Carleson theorem for the ball », Glasg. Math. J. 26 (1985), p. 13–17. Zbl 0576.32007 | MR 776671

[46] R. Rochberg« Decomposition theorems for Bergman spaces and their applications », in Operators and Function Theory, D. Reidel, 1985, p. 225–277. MR 810448

[47] W. RudinFunction Theory in the Unit Ball of n , Springer, New York, 1980. MR 601594

[48] J. Ryll & P. Wojtaszczyk« On homogeneous polynomials on a complex ball », Trans. Amer. Math. Soc. 276 (1983), p. 107–116. Zbl 0522.32004 | MR 684495

[49] K. Seip« Beurling type density theorems in the unit disk », Invent. Math. 113 (1993), p. 21–39. Zbl 0789.30025 | | MR 1223222

[50] —, « Regular sets of sampling and interpolation for weighted Bergman spaces », Proc. Amer. Math. Soc. 117 (1993), p. 213–220. Zbl 0763.30014 | MR 1111222

[51] J. Shapiro« Macey topologies, reproducing kernels and diagonal maps on Hardy and Bergman spaces », Duke Math. J. 43 (1976), p. 187–202. Zbl 0354.46036 | MR 500100

[52] J. Shi« Inequalities for integral means of holomorphic functions and their derivatives in the unit ball of n », Trans. Amer. Math. Soc. 328 (1991), p. 619–632.

[53] A. Siskakis« Weighted integrals of analytic functions », Acta Sci. Math. 66 (2000), p. 651–664. Zbl 0994.46008 | MR 1804215

[54] D. Stegenga« Multipliers of the Dirichlet space », Illinois J. Math. 24 (1980), p. 113–139. Zbl 0432.30016 | MR 550655

[55] E. Stein & G. Weiss« Interpolation of operators with change of measures », Trans. Amer. Math. Soc. 87 (1958), p. 159–172. Zbl 0083.34301 | MR 92943

[56] S. Stević« A generalization of a result of Choa on analytic functions with Hadamard gaps », J. Korean Math. Soc. 43 (2006), p. 579–591. Zbl 1101.32003 | MR 2218235

[57] M. StollInvariant Potential Theory in the Unit Ball of n , Cambridge Univ. Press, London, 1994. MR 1297545

[58] F. G. Tricomi & A. Erdelyi« The asymptotic expansion of a ratio of gamma functions », Pacific J. Math. 1 (1951), p. 133–142. Zbl 0043.29103 | MR 43948

[59] D. Ullrich« Radial divergence in BMOA », Proc. London Math. Soc. 68 (1994), p. 145–160. Zbl 0798.32008 | MR 1243839

[60] D. Vukotić« A sharp estimate for A α p functions in n », Proc. Amer. Math. Soc. 117 (1993), p. 753–756. Zbl 0773.32004 | MR 1120512

[61] Z. Wu« Carleson measures and multipliers for the Dirichlet space », J. Funct. Anal. 169 (1999), p. 148–163. Zbl 0962.30032 | MR 1726750

[62] H. Wulan & K. Zhu« Bloch and BMO functions in the unit ball », 53 (2008), p. 1009–1019, Complex Variables. Zbl 1157.32004 | MR 2460134

[63] —, « Lipschitz type characterizations of Bergman spaces », to appear in Bull. Canadian. Math. Soc. Zbl 1273.31003

[64] W. Yang & C. Ouyang« Exact location of α-Bloch spaces in L a p and H p of a complex unit ball », Rocky Mountain J. Math. 30 (2000), p. 1151–1169. Zbl 0978.32002 | MR 1797836

[65] R. ZhaoOn a general family of function spaces, vol. 105, Ann. Acad. Sci. Fenn. Math. Dissertationes, 1996, 56pp. MR 1395906

[66] K. Zhu« Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains », J. Operator Theory 20 (1988), p. 329–357. Zbl 0676.47016 | MR 1004127

[67] —, « Möbius invariant Hilbert spaces of holomorphic functions in the unit ball of n », Trans. Amer. Math. Soc. 323 (1991), 823-842). Zbl 0739.46009 | MR 982233

[68] —, « Bergman and Hardy spaces with small exponents », Pacific J. Math. 162 (1994), p. 189–199. Zbl 0798.32007 | MR 1247148

[69] —, « Holomorphic Besov spaces on bounded symmetric domains », Quart. J. Math. Oxford 46 (1995), p. 239–256. Zbl 0837.32013 | MR 1333834

[70] —, « Holomorphic Besov spaces on bounded symmetric domains II », Indiana Univ. Math. J. 44 (1995), p. 239–256. Zbl 0837.32013

[71] —, Spaces of Holomorphic Functions in the Unit Ball, Springer, New York, 2005.