Inequalities for holomorphic functions of several complex variables
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- by Jacob Burbea PDF
- Trans. Amer. Math. Soc. 276 (1983), 247-266 Request permission
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
- V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), 187β214. MR 157250, DOI 10.1002/cpa.3160140303
- Jacob Burbea, A Dirichlet norm inequality and some inequalities for reproducing kernel spaces, Proc. Amer. Math. Soc. 83 (1981), no.Β 2, 279β285. MR 624914, DOI 10.1090/S0002-9939-1981-0624914-0
- Jacob Burbea, Inequalities for reproducing kernel spaces, Illinois J. Math. 27 (1983), no.Β 1, 130β137. MR 684548
- William F. Donoghue Jr., Reproducing kernel spaces and analytic continuation, Rocky Mountain J. Math. 10 (1980), no.Β 1, 85β97. MR 573864, DOI 10.1216/RMJ-1980-10-1-85
- D. J. Newman and H. S. Shapiro, Certain Hilbert spaces of entire functions, Bull. Amer. Math. Soc. 72 (1966), 971β977. MR 205055, DOI 10.1090/S0002-9904-1966-11608-7
- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
- Saburou Saitoh, Some inequalities for analytic functions with a finite Dirichlet integral on the unit disc, Math. Ann. 246 (1979/80), no.Β 1, 69β77. MR 554132, DOI 10.1007/BF01352026
- Saburou Saitoh, Some inequalities for entire functions, Proc. Amer. Math. Soc. 80 (1980), no.Β 2, 254β258. MR 577754, DOI 10.1090/S0002-9939-1980-0577754-4 A. Selberg, Automorphic functions and integral operators, Seminars on Analytic Functions, Vol. II, Institute for Advanced Study, Princeton, N. J., 1957, 152-161.
- Ian N. Sneddon, Special functions of mathematical physics and chemistry, Oliver and Boyd, Edinburgh-London; Interscience Publishers, Inc., New York, 1956. MR 0080170
Additional Information
- © Copyright 1983 American Mathematical Society
- 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