Erratum to: Sharp Constant in Jackson’s Inequality with Modulus of Smoothness for Uniform Approximations of Periodic Functions
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DOI: 10.1134/s0001434618110421
Abstract: My paper contains an error. Namely, inequality (9) does not hold. For example, for k = 2,I do not know whether the error in the argument can be corrected and whether the main result of… read more here.
Keywords: constant jackson; sharp constant; erratum sharp; jackson inequality ... See more keywords
The sharp constant for the Burkholder–Davis–Gundy inequality and non-smooth pasting
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DOI: 10.3150/17-bej935
Abstract: We revisit the celebrated family of BDG-inequalities introduced by Burkholder, Gundy \cite{BuGu70} and Davis \cite{Da70} for continuous martingales. For the inequalities $\mathbb{E}[\tau^{\frac{p}{2}}] \leq C_p \mathbb{E}[(B^*(\tau))^p]$ with $0 < p < 2$ we propose a connection… read more here.
Keywords: constant burkholder; davis; sharp constant; non smooth ... See more keywords