The dual of the Bergman space 𝐴¹ in symmetric Siegel domains of type 𝐼𝐼

Békollé, David

doi:10.1090/S0002-9947-1986-0846599-X

The dual of the Bergman space $A^ 1$ in symmetric Siegel domains of type $\textrm {II}$
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Trans. Amer. Math. Soc. 296 (1986), 607-619 Request permission

Abstract:

An affirmative answer is given to the following conjecture of R. Coifman and R. Rochberg: in any symmetric Siegel domain of type II, the dual of the Bergman space ${A^1}$ coincides with the Bloch space of holomorphic functions and can be realized as the Bergman projection of ${L^\infty }$.

References

David Békollé, Le dual de la classe de Bergman $A^{1}$ dans le transformé de Cayley de la boule unité de $\textbf {C}^{n}$, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 9, 377–380 (French, with English summary). MR 703901
David Békollé, Le dual de la classe de Bergman $A^{1}$ dans le complexifié du cone sphérique, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 14, 581–583 (French, with English summary). MR 705166
David Békollé, Le dual de l’espace des fonctions holomorphes intégrables dans des domaines de Siegel, Ann. Inst. Fourier (Grenoble) 34 (1984), no. 3, 125–154 (French, with English summary). MR 762696, DOI 10.5802/aif.980
R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^{p}$, Representation theorems for Hardy spaces, Astérisque, vol. 77, Soc. Math. France, Paris, 1980, pp. 11–66. MR 604369
S. G. Gindikin, Analysis in homogeneous domains, Uspehi Mat. Nauk 19 (1964), no. 4 (118), 3–92 (Russian). MR 0171941
Adam Korányi and Joseph A. Wolf, Realization of hermitian symmetric spaces as generalized half-planes, Ann. of Math. (2) 81 (1965), 265–288. MR 174787, DOI 10.2307/1970616
François Trèves, Linear partial differential equations with constant coefficients: Existence, approximation and regularity of solutions, Mathematics and its Applications, Vol. 6, Gordon and Breach Science Publishers, New York-London-Paris, 1966. MR 0224958
Stephen Vági, Harmonic analysis on Cartan and Siegel domains, Studies in harmonic analysis (Proc. Conf., DePaul Univ., Chicago, Ill., 1974) MAA Stud. Math., Vol. 13, Math. Assoc. Amer., Washington, D.C., 1976, pp. 257–309. MR 0477178