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Boundary Interpolation for Continuous Holomorphic Functions

Published online by Cambridge University Press:  20 November 2018

William S. Cohn
William S. Cohn*
Affiliation:
Wayne State University, Detroit, Michigan
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Let Bn denote the unit ball in Cn with boundary S. We will be concerned with spaces of holomorphic functions on Bn and will use much of the notation and terminology found in W. Rudin's book [16]. Thus, if f is holomorphic in Bn and has homogeneous polynomial expansion

the radial derivative of f is given by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 5 , 01 October 1989 , pp. 769 - 785
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Adams, D., A note on the Choquet integrals with respect to Hausdorff capacity, preprint.Google Scholar
2. Adams, D., The classification problem for the capacities associated with the Besov and Triebel- Lizorkin spaces, preprint.Google Scholar
3. Ahern, P.and Nagel, A., Strong LP estimates for maximal functions with respect to singular measures; with applications to exceptional sets, Duke Math. J. 53 (1986), 359–393.Google Scholar
4. Ahern, P., Exceptional sets for holomorphic Sobolev functions, Mich. Math. J. 35 (1988), 29–41.Google Scholar
5. Aronszajn, N., F. Mulla and Szeptycki, P., On spaces of potentials connected with LP classes, Ann. Inst. Fourier 13 (1962), 211–306.Google Scholar
6. F. Beatrous and Burbea, J., Holomorphic Sobolev spaces on the ball, Dissertations Math., to appear.Google Scholar
7. L. Brown and Cohn, W., Some examples of cyclic vectors in the Dirichlet space, Proc. Amer. Math. Soc. 95 (1985), 42–46.Google Scholar
8. Cohn, W., Non-isotropic Hausdorff measure and exceptional sets for holomorphic Sobolev functions, Illinois J. Math., to appear.Google Scholar
9. Flett, T., The dual of an inequality of Hardy and Littlewood, J. Math. Analysis and Appl. 38 (1972), 746–765.Google Scholar
10. Frostman, O., Potential d'equilibre et capacité des emsembles avec quelques application a la théorie des fonctions, Medd. Lunds Univ. Math. Sem. 3 (1935), 115 pp.Google Scholar
11. Garnett, J., Bounded analytic functions (Academic Press, New York, 1981).Google Scholar
12. Koosis, P., A theorem of Khruschev and Pel 1er on restriction of analytic functions having finite Dirichlet integral to closed subsets of the unit circumference, Conference on Harmonic Analysis in Honor of Antoni Zygmund, Chicago, 1981 Vol. II, Wadsworth, Belmont, California (1983), 740–748.Google Scholar
13. V. G. Maz'ya and Shaposhnikova, T. O., Theory of multipliers in spaces of differentiable functions (Pitman Publishing, Marshfield, Mass., 1985).Google Scholar
14. Meyers, N. G., A theory of capacities for functions in Lebesgue spaces, Math. Scand. 26 (1970), 255–292.Google Scholar
15. Peller, V. V. and Khruschev, S. V., Hankel operators, best approximations and stationary Gaussian processes, Russian Math. Surveys 37 (1982), 61–144.Google Scholar
16. Rudin, W., Function theory in the unit ball of Cn (Springer-Verlag, New York, 1980).Google Scholar
17. T. Sjödin, Capacities of compact sets in linear subspaces of Rn, Pacific J. Math. 78 (1978), 261–266.Google Scholar
18. Stein, E., Singular integrals and differentiability properties of functions (Princeton Univ. Press, Princeton, 1970).Google Scholar
19. Wallin, H., Continuous functions and potential theory, Ark. Mat. 5 (1963), 55–84.Google Scholar