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Uniform Upper Bound for a Stable Measure of a Small Ball

   
@article{ECP995,
	author = {Michal Ryznar and Tomasz Zak},
	title = {Uniform Upper Bound for a Stable Measure of a Small Ball},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {3},
	year = {1998},
	keywords = {stable measure, small ball},
	abstract = {P. Hitczenko, S.Kwapien, W.N.Li, G.Schechtman, T.Schlumprecht and J.Zinn stated the following conjecture. Let $\mu$ be a symmetric $\alpha$-stable measure on a separable Banach space and $B$ a centered ball such that $\mu(B)\le b$. Then there exists a constant $R(b)$, depending only on $b$, such that $\mu(tB)\le R(b)t\mu(B)$ for all $0 < t < 1$. We prove that the above inequality holds but the constant $R$ must depend also on $\alpha$.},
	pages = {no. 9, 75-78},
	issn = {1083-589X},
	doi = {10.1214/ECP.v3-995},    
        url = {http://ecp.ejpecp.org/article/view/995}}