Finite unions of interpolation sequences

Duren, Peter; Schuster, Alexander

doi:10.1090/S0002-9939-02-06356-6

Finite unions of interpolation sequences
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by Peter Duren and Alexander P. Schuster PDF

Proc. Amer. Math. Soc. 130 (2002), 2609-2615 Request permission

Abstract:

A unified and relatively simple proof is given for some well-known results involving finite unions of uniformly separated sequences.

References

Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930. MR 117349, DOI 10.2307/2372840
Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547–559. MR 141789, DOI 10.2307/1970375
Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
Peter Duren, Dmitry Khavinson, and Harold S. Shapiro, Extremal functions in invariant subspaces of Bergman spaces, Illinois J. Math. 40 (1996), no. 2, 202–210. MR 1398090
John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
Charles Horowitz, Zeros of functions in the Bergman spaces, Duke Math. J. 41 (1974), 693–710. MR 357747
Charles Horowitz, Factorization theorems for functions in the Bergman spaces, Duke Math. J. 44 (1977), no. 1, 201–213. MR 427650
V. Kabaila, Interpolation sequences for the $H_{p}$ classes in the case $p<1$, Litovsk. Mat. Sb. 3 (1963), no. 1, 141–147 (Russian, with Lithuanian and English summaries). MR 0182735
Daniel H. Luecking, Inequalities on Bergman spaces, Illinois J. Math. 25 (1981), no. 1, 1–11. MR 602889
G. McDonald and C. Sundberg, Toeplitz operators on the disc, Indiana Univ. Math. J. 28 (1979), no. 4, 595–611. MR 542947, DOI 10.1512/iumj.1979.28.28042
Charles W. Neville, A short proof of an inequality of Carleson’s, Proc. Amer. Math. Soc. 65 (1977), no. 1, 131–132. MR 444958, DOI 10.1090/S0002-9939-1977-0444958-0
H. S. Shapiro, Comparative approximation in two topologies, Approximation theory (Papers, VIth Semester, Stefan Banach Internat. Math. Center, Warsaw, 1975) Banach Center Publ., vol. 4, PWN, Warsaw, 1979, pp. 225–232. MR 553768
H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513–532. MR 133446, DOI 10.2307/2372892