Tents and interpolating sequences in the unit ball
A sufficient condition is given to make a sequence of points interpolating for H∞(Bn). The methods are elementary: construction of the P. Beurling functions. This can be used to prove the sharpness of the exponent of Varopoulos’s necessary condition for interpolation. The result is also compared with Berndtsson’s recent sufficient condition, in conjunction with which it gives a slightly improved theorem.
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- Berndtsson, B., Interpolating sequences for H∞ in the ball, Nederl. Akad. Wetensch, Indag. Math. 88 (1985).Google Scholar
- Garnett, J., Bounded Analytic Functions, Academic Press, 1981.Google Scholar
- Mantero, A.M., Sur la condition de Carleson dans la boule unité de Cm, Boll. Un. Mat. Ital. (1983), 163–169.Google Scholar
- Rudin, W., Function Theory in the Unit Ball of ℂ n, Springer-Verlag, 1980.Google Scholar
- Thomas, P.J., Interpolating sequences of complex hyperplanes in the unit ball of Cn, to appear in Ann. Inst. Fourier (Grenoble) 36 (1986), No. 4.Google Scholar