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Riesz's Functions in Weighted Hardy and Bergman Spaces

  • Takahiko Nakazi (a1) and Masahiro Yamada (a2)

Abstract

Let μ be a finite positive Borel measure on the closed unit disc . For each a in , put where ƒ ranges over all analytic polynomials with f(a) = 1. This upper semicontinuous function S(a) is called a Riesz's function and studied in detail. Moreover several applications are given to weighted Bergman and Hardy spaces.

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References

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1. Bourdon, P.S. and Shapiro, J.H., Spectral synthesis and common cyclic vectors, Michigan Math., J. 37(1990), 7190.
2. Brennan, J.E., Weighted polynomial approximation, quasianalyticity and analytic continuation, J. fur, Mathematik. 357(1984), 2350.
3. Conway, J.B., Subnormal operators, Research Notes in Mathematics 51, Pitman Advanced Publishing Program, 1981.
4. Gohberg, I., Goldberg, S. and Kasshoek, M.A., Classes of linear operators I, Operator Theory: Advances and Applications, 49, Birkhauser Verlag, Basel, 1990.
5. Grenanderand, U. Szegő, G., Toeplitz forms and their applications, Chelsea Publishing Company, 1984.
6. Koosis, P., The logarithmic integral I, Cambridge Studies in Advanced Mathematics 12, Cambridge University Press, Cambridge-New York, 1988.
7. Kriete, T. and Trent, T., Growth near the boundary in H2(μ) spaces, Proc. Amer. Math., Soc. 62(1977), 8388.
8. Nakazi, T. and Yamada, M., ﹛Aj)-conditions and Carleson inequalities in Bergman spaces, Pacific J., Math. 173(1996), 151171.
9. Rochberg, R., Toeplitz operators on weighted hP spaces, Indiana Univ. Math., J. 26(1977), 291298.
10. Rosenblum, M., Summability of Fourier series in LP(dμ), Trans. Amer. Math., Soc. 105(1962), 3242.
11. Rudin, W., Functional analysis, McGraw-Hill Book Company, 1973.
12. Srinivasan, T.P. and Wang, J.K., Weak*-Dirichlet algebras. In: Function Algebras (Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965., Scott-Foresman, Chicago, 111., 1966. 216249.
13. Yamada, M., Weighted Bergman space and Szegő s infimum, preprint.
14. Zhu, K., Operator theory in function spaces, Pure and Applied Mathematics, Marcel Dekker, Inc., New York and Basel, 1990.
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Riesz's Functions in Weighted Hardy and Bergman Spaces

  • Takahiko Nakazi (a1) and Masahiro Yamada (a2)

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