Duality theorems for Hardy and Bergman spaces on convex domains of finite type in n
Annales de l'Institut Fourier, Volume 45 (1995) no. 5, pp. 1305-1327.

We study Hardy, Bergman, Bloch, and BMO spaces on convex domains of finite type in n-dimensional complex space. Duals of these spaces are computed. The essential features of complex domains of finite type, that make these theorems possible, are isolated.

Nous étudions les espaces de Hardy, Bergman, Bloch et BMO pour des domaines convexes de type fini dans n . Nous calculons les duaux de ces espaces et nous mettons en lumière les propriétés essentielles des domaines complexes de type fini, qui rendent ces théorèmes possibles.

@article{AIF_1995__45_5_1305_0,
     author = {Krantz, Steven G. and Li, Song-Ying},
     title = {Duality theorems for {Hardy} and {Bergman} spaces on convex domains of finite type in ${\mathbb {C}}^n$},
     journal = {Annales de l'Institut Fourier},
     pages = {1305--1327},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {45},
     number = {5},
     year = {1995},
     doi = {10.5802/aif.1497},
     zbl = {0835.32004},
     mrnumber = {96m:32002},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1497/}
}
TY  - JOUR
TI  - Duality theorems for Hardy and Bergman spaces on convex domains of finite type in ${\mathbb {C}}^n$
JO  - Annales de l'Institut Fourier
PY  - 1995
DA  - 1995///
SP  - 1305
EP  - 1327
VL  - 45
IS  - 5
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1497/
UR  - https://zbmath.org/?q=an%3A0835.32004
UR  - https://www.ams.org/mathscinet-getitem?mr=96m:32002
UR  - https://doi.org/10.5802/aif.1497
DO  - 10.5802/aif.1497
LA  - en
ID  - AIF_1995__45_5_1305_0
ER  - 
%0 Journal Article
%T Duality theorems for Hardy and Bergman spaces on convex domains of finite type in ${\mathbb {C}}^n$
%J Annales de l'Institut Fourier
%D 1995
%P 1305-1327
%V 45
%N 5
%I Association des Annales de l’institut Fourier
%U https://doi.org/10.5802/aif.1497
%R 10.5802/aif.1497
%G en
%F AIF_1995__45_5_1305_0
Krantz, Steven G.; Li, Song-Ying. Duality theorems for Hardy and Bergman spaces on convex domains of finite type in ${\mathbb {C}}^n$. Annales de l'Institut Fourier, Volume 45 (1995) no. 5, pp. 1305-1327. doi : 10.5802/aif.1497. https://aif.centre-mersenne.org/articles/10.5802/aif.1497/

[BA] S. Ross Barker, Two theorems on boundary values of analytic functions, Proc. A.M.S., 68 (1978), 54-58. | MR: 58 #17211 | Zbl: 0378.32011

[BEA] F. Beatrous, Lp estimates for extensions of holomorphic functions, Michigan Math. J., 32 (1985), 361-380. | MR: 87b:32023 | Zbl: 0584.32024

[BL] F. Beatrous and S.-Y. Li, On the boundedness and Compactness of operators of Hankel type, J. Funct. Anal., vol. 111 (1993), 350-379. | MR: 94b:47033 | Zbl: 0793.47022

[B] H. P. Boas, The Szegö projection, Sobolev estimates in the regular domain, Trans. A.M.S., 300 (1987), 109-132. | Zbl: 0622.32006

[BEL] S. Bell, Extendibility of Bergman kernel function, Complex analysis II, Lecture Notes in Math., 1276, 33-41, Berlin-Heidelberg-New York. | MR: 89b:32032 | Zbl: 0626.32028

[C] D. Catlin, Subelliptic estimates for the ∂-Neumann problem, Ann. Math., 126 (1987), 131-192. | MR: 88i:32025 | Zbl: 0627.32013

[CW] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bulletin A.M.S., 83 (1977), 569-643. | MR: 56 #6264 | Zbl: 0358.30023

[CHE] L. Chen, Ph.D. Thesis, Univ. of California at Irvine, 1994.

[CHR] M. Christ, Lectures on Singular Integral Operators, Conference Board of Mathematical Sciences, American Mathematical Society, Providence, 1990. | Zbl: 0745.42008

[COU] B. Coupet, Régularité d'applications holomorphes sur des variétés totalement réelles, Thèse, Université de Provence, 1987.

[CRW] R. Coifman, R. Rochberg, and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. Math., 103 (1976), 611-635. | MR: 54 #843 | Zbl: 0326.32011

[DAF] G. Dafni, Hardy spaces on some pseudoconvex domains, Jour. Geometric Analysis, (1995). | Zbl: 0802.32012

[F] C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math., 26 (1974), 1-65. | MR: 50 #2562 | Zbl: 0289.32012

[FS] C. Fefferman and E. M. Stein, Hp spaces of several variables, Acta Math., 129 (1972), 137-193. | MR: 56 #6263 | Zbl: 0257.46078

[H] L. Hörmander, Lp estimates for pluri-subharmonic functions, Math. Scand., 20 (1967), 65-78. | Zbl: 0156.12201

[KER] N. Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann., 195 (1972), 149-158.

[K1] S. Krantz, Function Theory of Several Complex Variables, 2nd. ed., Wadsworth, Belmont, 1992. | MR: 93c:32001 | Zbl: 0776.32001

[K2] S. Krantz, Invariant metrics and the boundary behavior of holomorphic functions, Jour. of Geometric Analysis, 1 (1991), 71-97. | MR: 92f:32007 | Zbl: 0728.32002

[K3] S. Krantz, Holomorphic functions of bounded mean oscillation and mapping properties of the Szegö projection, Duke Math. J., 47 (1980), 743-761. | MR: 82i:32010 | Zbl: 0456.32004

[KL1] S. Krantz and S.-Y. Li, A note on Hardy spaces and functions of bounded mean oscillation on domains in ℂn, Michigan Math. Jour., 41 (1994), 51-72. | MR: 95f:32008 | Zbl: 0802.32013

[KL2] S. Krantz and S.-Y. Li, On the Decomposition Theorems for Hardy Spaces in Domains in ℂn and Applications, J. of Fourier Anal. and Appl., to appear. | Zbl: 0886.32003

[MCN1] J. Mcneal, Convex domains of finite type, Jour. Funct. Anal., 108 (1992), 361-373. | MR: 93h:32020 | Zbl: 0777.31007

[MCN2] J. Mcneal, Estimates on the Bergman kernels of convex domains, Advances in Math., 109 (1994), 108-139. | MR: 95k:32023 | Zbl: 0816.32018

[MS1] J. D. Mcneal and E. M. Stein, Mapping properties of the Bergman projection on convex domains of finite type, Duke Math. J., 73 (1994), 177-199. | MR: 94k:32037 | Zbl: 0801.32008

[MS2] J. D. Mcneal and E. M. Stein, The Szegö projection on convex domains, preprint. | Zbl: 0948.32004

[NSW] A. Nagel, E. M. Stein, and S. Wainger, Balls and metrics defined by vector fields. I. Basic properties, Acta Math., 155 (1985), 103-147. | MR: 86k:46049 | Zbl: 0578.32044

[NRSW] A. Nagel, J.P. Rosay, E.M. Stein, and S. Wainger, Estimates for the Bergman and Szegö kernels in ℂ2, Ann. Math., 129 (1989), 113-149. | MR: 90g:32028 | Zbl: 0667.32016

[ST1] E.M. Stein, Singular integral and differentiability properties of functions, Princeton University Press, 1970. | MR: 44 #7280 | Zbl: 0207.13501

[ST2] E. M. Stein, Boundary Behavior of Holomorphic Functions of Several Complex Variables, Princeton University Press, Princeton, 1972. | MR: 57 #12890 | Zbl: 0242.32005

Cited by Sources: