# A probabilistic version of Rosenthal’s inequality

@inproceedings{Astashkin2013APV, title={A probabilistic version of Rosenthal’s inequality}, author={Sergey V. Astashkin and Konstantin E. Tikhomirov}, year={2013} }

k=1 m{t ∈ [0, 1] : |fk(t)| > τ} (τ > 0), where m is the Lebesgue measure. Let F ∗(t) be the non-increasing left-continuous rearrangement of F (t) and, as usual, χA be the characteristic function of a set A. In [1, Theorem 1], Johnson and Schechtman proved that for every quasi-normed rearrangement invariant (r.i.) space X on [0, 1] and for the arbitrary sequence {fk}k=1 ⊂ X (n ∈ N) of non-negative independent functions, the following inequality holds:

## 3 Citations

Randomized Operators on $${n\times n}$$n×n Matrices and Applications

- Mathematics
- 2016

Some combinatorial and probabilistic estimates motivated by earlier works due to S. Kwapien and C. Schütt are proved. We study these estimates in the general setting of rearrangement invariant…

ROSENTHAL’S INEQUALITIES: ∆−NORMS AND QUASI-BANACH SYMMETRIC SEQUENCE SPACES

- Mathematics
- 2019

Let X be a symmetric quasi-Banach function space with Fatou property and let E be an arbitrary symmetric quasi-Banach sequence space. Suppose that (fk)k≥0 ⊂ X is a sequence of independent random…

Rosenthal’s inequalities: ${\Delta }$-norms and quasi-Banach symmetric sequence spaces

- Mathematics
- 2019

Let $X$ be a symmetric quasi-Banach function space with Fatou property and let $E$ be an arbitrary symmetric quasi-Banach sequence space. Suppose that $(f_k)_{k\geq0}\subset X$ is a sequence of…

## References

SHOWING 1-10 OF 13 REFERENCES

The Optimal Order for the p-th Moment of Sums of Independent Random Variables with Respect to Symmetric Norms and Related Combinatorial Estimates

- Mathematics
- 2002

AbstractFor n independent random variables f1, . . . ,fn and a symmetric norm || ||X on ℝn, we show that for 1≤ p < ∞
Here
is the disjoint sum of the fi's and h* is the non-increasing…

Series of independent random variables in rearrangement invariant spaces: An operator approach

- Mathematics
- 2005

This paper studies series of independent random variables in rearrangement invariant spacesX on [0, 1]. Principal results of the paper concern such series in Orlicz spaces exp(Lp), 1≤p≤∞ and Lorentz…

Rearrangement invariant norms of symmetric sequence norms of independent sequences of random variables

- Mathematics
- 2001

LetX1,X2, …,Xn be a sequence of independent random variables, letM be a rearrangement invariant space on the underlying probability space, and letN be a symmetric sequence space. This paper gives an…

Series of independent, mean zero random variables in rearrangement-invariant spaces having the Kruglov property

- Mathematics
- 2008

This paper compares sequences of independent, mean zero random variables in a rearrangement-invariant space X on [0, 1] with sequences of disjoint copies of individual terms in the corresponding…

On the subspaces ofLp(p>2) spanned by sequences of independent random variables

- Mathematics
- 1970

Let 2<p<∞. The Banach space spanned by a sequence of independent random variables inLp, each of mean zero, is shown to be isomorphic tol2,lp,l2⊕lp, or a new spaceXp, and the linear topological…

Measuring the magnitude of sums of independent random variables

- Mathematics
- 1999

This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Levy…

Classical Banach spaces

- Education
- 1973

Springer-Verlag is reissuing a selected few of these highly successful books in a new, inexpensive sofcover edition to make them easily accessible to younger generations of students and researchers.

RESONANCE THEOREMS and SUPERLINEAR OPERATORS

- Mathematics
- 1970

This article is concerned with problems of the metrical theory of functions. We establish criteria for systems of measurable functions to be systems of convergence in measure, systems of convergence…