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Transactions of the American Mathematical Society

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Inequalities for holomorphic functions of several complex variables


Author: Jacob Burbea
Journal: Trans. Amer. Math. Soc. 276 (1983), 247-266
MSC: Primary 32H10; Secondary 32A10, 46E20
DOI: https://doi.org/10.1090/S0002-9947-1983-0684506-0
MathSciNet review: 684506
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Abstract: Sharp norm-inequalities, valid for functional Hilbert spaces of holomorphic functions on the polydisk, unit ball and $ {{\mathbf{C}}^n}$ are established by using the notion of reproducing kernels. These inequalities extend earlier results of Saitoh and ours.


References [Enhancements On Off] (What's this?)

  • [1] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform. I, Comm. Pure Appl. Math. 14 (1961), 187-214. MR 0157250 (28:486)
  • [2] J. Burbea, A Dirichlet norm inequality and some inequalities for reproducing kernel spaces, Proc. Amer. Math. Soc. 83 (1981), 279-285. MR 624914 (82j:30014)
  • [3] -, Inequalities for reproducing kernel spaces, Illinois J. Math. 27 (1983). MR 684548 (84a:30017)
  • [4] W. F. Donoghue, Jr., Reproducing kernel spaces and analytic continuation, Rocky Mountain J. Math. 10 (1980), 85-97. MR 573864 (81j:32027)
  • [5] D. J. Newman and H. S. Shaprio, Certain Hilbert spaces of entire functions, Bull. Amer. Math. Soc. 72 (1966), 971-977. MR 0205055 (34:4890)
  • [6] W. Rudin, Function theory in the unit ball of $ {{\mathbf{C}}^n}$, Springer-Verlag, New York, 1980. MR 601594 (82i:32002)
  • [7] S. Saitoh, Some inequalities for analytic functions with a finite Dirichlet integral on the unit disk, Math. Ann. 246 (1979), 69-77. MR 554132 (80j:30005)
  • [8] -, Some inequalities for entire functions, Proc. Amer. Math. Soc. 80 (1980), 254-258. MR 577754 (81i:30049)
  • [9] A. Selberg, Automorphic functions and integral operators, Seminars on Analytic Functions, Vol. II, Institute for Advanced Study, Princeton, N. J., 1957, 152-161.
  • [10] I. N. Sneddon, Special functions of mathematical physics and chemistry, Oliver and Boyd, Edinburgh, 1961. MR 0080170 (18:204a)

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DOI: https://doi.org/10.1090/S0002-9947-1983-0684506-0
Article copyright: © Copyright 1983 American Mathematical Society

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