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Duality and differential operators on the Bergman spaces of bounded symmetric domains. (English) Zbl 0782.47028

The author investigates some differential operators defined on an irreducible bounded symmetric domain \(D\) of tube type in \(\mathbb{C}\), and uses them to describe the dual and predual of the Bergman space \(L^ 1_ a(D)\). The main results are expressed by theorems \(A\) and \(B\). Their proofs are based on other 15 lemmas, theorems and corollaries.
Reviewer: I.Gottlieb (Iaşi)

MSC:

47B38 Linear operators on function spaces (general)
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
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References:

[1] Axler, S., Bergman spaces and their operators, (Lecture Notes at the Indiana University Function Theoretic Operator Theory Conference (November 1985)) · Zbl 0681.47006
[2] Békollé, D., The dual of the Bergman space \(A^1\) in symmetric Siegel domains of type II, Trans. Amer. Math. Soc., 607-619 (1986) · Zbl 0626.32033
[3] Dib, H., (Thesis (1988), Université Louis Pasteur)
[4] Faraut, J.; Korányi, A., Function spaces and reproducing kernels on bounded symmetric domains, J. Funct. Anal., 88, 64-89 (1990) · Zbl 0718.32026
[5] Korányi, A., Complex Analysis and Symmetric Domains (1988), Ecole CIMPA-Université de Poitiers
[6] Nomura, T., Algebraically independent generators of invariant differential operators on a symmetric cone, J. Reine Angew. Math., 400, 122-133 (1989) · Zbl 0667.43007
[7] Rudin, W., Function Theory in the Unit Ball of \(C^n (1980)\), Springer: Springer New York
[8] Upmeier, H., Jordan algebras and harmonic analysis on symmetric spaces, Amer. J. Math., 108, 1-25 (1986) · Zbl 0603.46055
[9] Zhu, K. H., Duality and Hankel operators on the Bergman spaces of bounded symmetric domains, J. Funct. Anal., 81, 260-278 (1988) · Zbl 0669.47019
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