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Integral means on radially weighted spaces of analytic functions

Part of: Miscellaneous topics of analysis in the complex domain Normed linear spaces and Banach spaces; Banach lattices Spaces and algebras of analytic functions

Published online by Cambridge University Press:  09 April 2009

Mats Erik Andersson
Mats Erik Andersson
Affiliation:
Department of Mathematics, Kungliga Tekniska Högskolan, Lindstedtsvägen 25, S -100 44 Stockholm, Sweden e-mail: matsa@math. kth.se
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Abstract

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Hilbert spaces of analytic functions generated by rotationally symmetric measures on disks and annuli are studied. A domination relation between function norm and weighted sums of integral means on circles is developed. The function norm and the weighted sum take the same value for a specified class of polynomials. This class can be varied according to two parameters. Parts of the construction carry over to other Banach spaces of analytic of harmonic functions. Counterexamples illuminating properties of the complex method of interpolation appear as a byproduct.

Keywords

Bergman spcesinterpolating polynomialsGuass-Jacobi quadraturemoment sequencecomplex method of interpolation.

MSC classification

Secondary: 30H05: Bounded analytic functions 30E05: Moment problems, interpolation problems 46B70: Interpolation between normed linear spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 1 , August 1998 , pp. 68 - 83
Copyright
Copyright © Australian Mathematical Society 1998

References

[A]Andersson, M. E., ‘Integral means on Bergman spaces’, Complex Variables Theory Appl. 132 (1997), 147–160.Google Scholar
[F]Freud, G., Orthogonale Polynome, Mathematische Reihe, Band 33 (Birkhäuser, Basel, 1969).CrossRefGoogle Scholar
[Ko]Korenblum, B., ‘A maximum principle for the Bergman space’, Publ. Mat. 35 (1991), 479–486.Google Scholar
[KORZ]Korenblum, B., O'Neil, R., Richards, K. and Zhu, K. ‘Totally monotone functions with applications to the Bergman space’, Trans. Amer. Math. Soc. 337 (1993), 795–806.Google Scholar
[KR]Korenblum, B. and Richards, K., ‘Majorization and domination in the Bergman space’, Proc. Amer. Math. Soc. 117 (1993), 153–158.Google Scholar
[Kr]Krylov, V., Approximate calculation of integrals (transl. Stroud, A.) (Macmillan, New York, 1962).Google Scholar
[M]Matero, J., ‘On Korenblum's maximum principle for Bergman space’, Arch. Math. 64 (1995), 337–340.CrossRefGoogle Scholar
[PS]Polya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis II (Springer, Berlin, 1971).Google Scholar
[S]Schwick, W., ‘On Korenblum's maximum principle’, Proc. Amer. Math. Soc. 125 (1997), 2581–2588.Google Scholar