Maximal inequalities for continuous martingales and their differential subordinates
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- by Adam Osȩkowski PDF
- Proc. Amer. Math. Soc. 139 (2011), 721-734 Request permission
Abstract:
Let $X=(X_t)_{t\geq 0}, Y=(Y_t)_{t\geq 0}$ be continuous-path martingales such that $Y$ is differentially subordinate to $X$. The paper contains the proofs of the sharp inequalities \[ \sup _{t\geq 0}||Y_t||_p \leq \sqrt {\frac {2}{p}} ||\sup _{t\geq 0}|X_t| ||_p, \quad 1\leq p< 2\] and \[ \sup _{t\geq 0}||Y_t||_p \leq (p-1) ||\sup _{t\geq 0}|X_t| ||_p, \quad 2\leq p<\infty .\]References
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Additional Information
- Adam Osȩkowski
- Affiliation: Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
- ORCID: 0000-0002-8905-2418
- Email: ados@mimuw.edu.pl
- Received by editor(s): June 29, 2009
- Received by editor(s) in revised form: April 14, 2010
- Published electronically: August 13, 2010
- Additional Notes: The author was partially supported by the Foundation for Polish Science and MNiSW Grant N N201 397437
- Communicated by: Richard C. Bradley
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 721-734
- MSC (2010): Primary 60G44; Secondary 60H05
- DOI: https://doi.org/10.1090/S0002-9939-2010-10539-7
- MathSciNet review: 2736351