On the integral means of derivatives of the atomic function
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- by Miodrag Mateljević and Miroslav Pavlović
- Proc. Amer. Math. Soc. 86 (1982), 455-458
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671214-X
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Abstract:
In this note we give upper and lower estimates on integral means of the atomic function and its derivatives over a circle of radius $r$ as $r$ approaches 1. From this we derive some known and new results.References
- Patrick Ahern, The mean modulus and the derivative of an inner function, Indiana Univ. Math. J. 28 (1979), no. 2, 311–347. MR 523107, DOI 10.1512/iumj.1979.28.28022
- P. R. Ahern and D. N. Clark, On inner functions with $B^{p}$ derivative, Michigan Math. J. 23 (1976), no. 2, 107–118. MR 414884, DOI 10.1307/mmj/1029001659
- H. A. Allen and C. L. Belna, Singular inner functions with derivative in $B^{p}$, Michigan Math. J. 19 (1972), 185–188. MR 299796, DOI 10.1307/mmj/1029000852
- Charles L. Belna and Benjamin Muckenhoupt, The derivative of the atomic function is not in $B^{2/3}$, Proc. Amer. Math. Soc. 63 (1977), no. 1, 129–130. MR 586555, DOI 10.1090/S0002-9939-1977-0586555-2
- Michael R. Cullen, Derivatives of singular inner functions, Michigan Math. J. 18 (1971), 283–287. MR 283205
- F. Holland and J. B. Twomey, On Hardy classes and the area function, J. London Math. Soc. (2) 17 (1978), no. 2, 275–283. MR 486532, DOI 10.1112/jlms/s2-17.2.275
- F. Holland and J. B. Twomey, Conditions for membership of Hardy spaces, Aspects of contemporary complex analysis (Proc. NATO Adv. Study Inst., Univ. Durham, Durham, 1979) Academic Press, London-New York, 1980, pp. 425–433. MR 623486
- Miroljub Jevtić, Sur la dérivée de la fonction atomique, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 3, 201–203 (French, with English summary). MR 610319
- Miodrag Mateljević and Miroslav Pavlović, $L^{p}$-behavior of power series with positive coefficients and Hardy spaces, Proc. Amer. Math. Soc. 87 (1983), no. 2, 309–316. MR 681840, DOI 10.1090/S0002-9939-1983-0681840-0 —, On weighted ${L^p}$ norms of area and length functions for analytic functions and Bergman spaces, Mat. Vesnik (to appear).
- Christian Pommerenke, Über die Mittelwerte und Koeffizienten multivalenter Funktionen, Math. Ann. 145 (1961/62), 285–296 (German). MR 133448, DOI 10.1007/BF01451371
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 455-458
- MSC: Primary 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671214-X
- MathSciNet review: 671214