EUDML

For random variables $S = \sum_{i = 1}^{\infty} α_{i} ξ_{i}$ , where $(ξ_{i})$ is a sequence of symmetric, independent, identically distributed random variables such that $l n P (| ξ_{i} | \geq t)$ is a concave function we give estimates from above and from below for the tail and moments of S. The estimates are exact up to a constant depending only on the distribution of ξ. They extend results of S. J. Montgomery-Smith [MS], M. Ledoux and M. Talagrand [LT, Chapter 4.1] and P. Hitczenko [H] for the Rademacher sequence.

N. Aronszajn; L. Gross; S. Kwapień; N. Nielsen; A. Pełczyński; A. Pietsch; L. Schwartz; P. Saphar; S. Chevet; R. Dudley; D. Garling; N. Kalton; B. Mitjagin; S. Rolewicz; E. Schock; J. Daleckiĭ; J. Dobrakov; B. Gelbaum; G. Henkin; L. Nachbin; N. Peck; L. Waelbroeck; P. Porcelli; M. Rao; M. Zerner; V. Zakharjuta — 1970

Studia Mathematica

1. The operator ideals and measures in linear spaces 469-472 2. Schauder bases and linear topological invariants 473-478 3. Various problems 479-483

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Isomorphic characterizations of Hilbert spaces by orthogonal series with vector valued coefficients

Enflo's example of a Banach space without the approximation property

Sur l'intégrabilité de norme dans un espace de Banach

Comments to Enflo's construction of Banach space without the approximation property

Sums of independent Banach space valued random variables (after J. Hoffmann-Jørgensen)

An analytic approach to semiclassical potential theory

A remark on p-absolutely summing operators in $l_{r}$ -spaces

Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients

A linear topological characterization of inner-product spaces

On a theorem of L. Schwartz and its applications to absolutely summing operators

On Banach spaces containing $c_{0}$ . A supplement to the paper by J.Hoffman-Jørgensen “Sums of independent Banach space valued random variables”

Some remarks on (p,q)-absolutely summing operators in $l_{p}$ -spaces

Some linear topological properties of the hardy spaces $𝐇^{p}$

The main triangle projection in matrix spaces and its applications

Tail and moment estimates for sums of independent random variables with logarithmically concave tails

Discontinuous invariant functio- nals and traces

Mackey continuity of characteristic functionals.

A proof of a conjecture of Bobkov and Houdré.

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