Published 2017
| Submitted
Journal Article
Open
Makarov's principle for the Bloch unit ball
- Creators
- Ivrii, O. V.
- Kayumov, I. R.
Abstract
Makarov's principle relates three characteristics of Bloch functions that resemble the variance of a Gaussian: asymptotic variance, the constant in Makarov's law of iterated logarithm and the second derivative of the integral means spectrum at the origin. While these quantities need not be equal in general, we show that the universal bounds agree if we take the supremum over the Bloch unit ball. For the supremum (of either of these quantities), we give the estimate Σ^2_B < min(0.9, Σ^2), where Σ^2 is the analogous quantity associated to the unit ball in the L∞ norm on the Bloch space. This improves on the upper bound in Pommerenke's estimate 0.685^2 < Σ^2_B ⩽ 1.
Additional Information
© 2017 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. Received 1 May 2016. The first author was supported by the Academy of Finland, project nos. 271983 and 273458. The second author was supported by the RFBR and the government of the Republic of Tatarstan, project nos. 14-01-00351 and 15-41-02433.Attached Files
Submitted - 1605.00246.pdf
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Additional details
- Eprint ID
- 78065
- Resolver ID
- CaltechAUTHORS:20170609-134523950
- 271983
- Academy of Finland
- 273458
- Academy of Finland
- Russian Foundation for Basic Research
- 14-01-00351
- Republic of Tatarstan
- 15-41-02433
- Republic of Tatarstan
- Created
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2017-06-09Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field