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A Note on Blaschke Products with Zeroes in a Nontangential Region

Published online by Cambridge University Press:  20 November 2018

Miroljub Jevtić
Miroljub Jevtić*
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
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Abstract

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We show that if B is α Blaschke product with nontangential zero set {zk} and 0 < p < 1, 1/2 < αp < 1, then the condition sup0<r<1(l — r) Mp(r, D1+αB) < ∞ is equivalent to the condition {(1 - |zk|(1/p)-αKα} ∊ l∞.

Keywords

30D50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 18 - 23
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Ahern, P., Clark, D., On inner functions with Hp derivative, Michigan Math. J. 21 (1974), pp. 115–127. Google Scholar
2. Ahern, P., M. Jevtić, Mean Modulus and the Fractional Derivative of an Inner Function, Complex Variables 3 (1984), pp. 431–445. Google Scholar
3. Duren, P., Theory of Hp spaces, Academic Press, New York, 1970.Google Scholar
4. Flett, T., The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Analysis and Appl. 38 (1972), pp. 746–765. Google Scholar
5. Kim, H., Derivatives of Blaschke products, Pacific J. Math. 114 (1984), pp. 175–190.Google Scholar
6. Verbitski, J., On Taylor coefficients and LP -continuity moduli of Blaschke products, LOMI, Leningrad Seminar Notes 107 (1982), pp. 27–35.Google Scholar
7. Verbitski, J., Inner functions, Besov spaces and multipliers, DAN SSSR, 276 (1984), No. 1, pp. 11–14. Soviet Math. Doklady, Vol. 29, No. 3 (1984), AMS translation.Google Scholar