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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 11, Fasc. 2,
pages 271 - 285
 

ON DENSITY OF A STABLE UNIFORMLY CONVEX NORM

Michał Ryznar

Abstract: Let (E,||.||) be a uniformly convex Banach space and assume that its modulus of uniform convexity a(.) satisfies the condition: a(e) > const.en, n (- N. We prove that for every stable symmetric measure m on E the density of the distribution function F (t) = m(|| .+z ||< t), z z (- E is bounded on every interval (0,T), T > 0. Under some additional assumptions we extend the conclusion to the whole half-line (0, oo ).

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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