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Research Papers
Sharp bounds for distribution of martingale transform of bounded functions
M. I. Novikov Saint Petersburg State University
Abstract:
The paper suggests a characterization of positive function $ f $ such that $ f(\psi_\infty) $ is summable for any limit value $ \psi_\infty $ of the martingale transform for an indicator function. The characterizing condition is that a version of the Lipschitz majorant of $ f $ is summable with respect to an exponential weight. The reasoning is based on the calculation of particular minimal biconcave functions on the strip.
Keywords:
Burkholder's method, biconcave functions, Bellman function, martingale transform, Stein–Weiss formula.
Received: 11.03.2024
Citation:
M. I. Novikov, “Sharp bounds for distribution of martingale transform of bounded functions”, Algebra i Analiz, 36:4 (2024), 57–147
Linking options:
https://www.mathnet.ru/eng/aa1929 https://www.mathnet.ru/eng/aa/v36/i4/p57
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Statistics & downloads: |
Abstract page: | 132 | Full-text PDF : | 3 | References: | 27 | First page: | 15 |
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