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Sharp Inequalities for Linear Combinations of Orthogonal Martingales.
- Source :
-
Frontiers of Mathematics . May2024, Vol. 19 Issue 3, p419-433. 15p. - Publication Year :
- 2024
-
Abstract
- For any two real-valued continuous-path martingales X = {Xt}t≥0 and Y = {Yt}t≥0, with X and Y being orthogonal and Y being differentially subordinate to X, we obtain sharp Lp inequalities for martingales of the form aX + bY with a, b real numbers. The best Lp constant is equal to the norm of the operator aI + bH from Lp to Lp, where H is the Hilbert transform on the circle or real line. The values of these norms were found by Hollenbeck, Kalton and Verbitsky [Studia Math., 2003, 157(3): 237–278]. We also give applications of our martingale inequalities to Riesz transforms and some discrete operators. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MARTINGALES (Mathematics)
*REAL numbers
*HILBERT transform
Subjects
Details
- Language :
- English
- ISSN :
- 27318648
- Volume :
- 19
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Frontiers of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176997890
- Full Text :
- https://doi.org/10.1007/s11464-022-0116-0