Inequalities for holomorphic functions of several complex variables

Burbea, Jacob

doi:10.1090/S0002-9947-1983-0684506-0

Inequalities for holomorphic functions of several complex variables
HTML articles powered by AMS MathViewer

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), 187–214. 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. 2, 279–285. MR 624914, DOI 10.1090/S0002-9939-1981-0624914-0
Jacob Burbea, Inequalities for reproducing kernel spaces, Illinois J. Math. 27 (1983), no. 1, 130–137. MR 684548
William F. Donoghue Jr., Reproducing kernel spaces and analytic continuation, Rocky Mountain J. Math. 10 (1980), no. 1, 85–97. 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), 971–977. 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. 1, 69–77. MR 554132, DOI 10.1007/BF01352026
Saburou Saitoh, Some inequalities for entire functions, Proc. Amer. Math. Soc. 80 (1980), no. 2, 254–258. MR 577754, DOI 10.1090/S0002-9939-1980-0577754-4

Automorphic functions and integral operators

Ian N. Sneddon, Special functions of mathematical physics and chemistry, Oliver and Boyd, Edinburgh-London; Interscience Publishers, Inc., New York, 1956. MR 0080170