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Bounds on the tail probability of u-statistics and quadratic forms
(2011)
The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear k-correlations of n > k independent random variables.
On a weak type (1, 1) inequality for a maximal conjugate function
(2011)
In a celebrated paper, Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of Hp spaces for 0 < p < ∞. In this paper, we show that their method extends to higher dimensions ...
Comparison of sums of independent identically distributed random variables
(2011)
Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ∥Sk∥ with that of ∥Sj∥, and deduce some tail distribution maximal ...
Inequalities of correlation type for symmetric stable random vectors
(2011)
We point out a certain class of functions f and g for which random variables f(X1,...,Xm) and g(Xm+1,...,Xk) are non-negatively correlated for any symmetric jointly stable random variables Xi. We also show another result ...
Finite time blow up for a Navier-Stokes like equation
(2011)
We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a ...
Complemented subspaces of spaces obtained by interpolation
(2011)
If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A0,A1) such that A0 and A1 are isometric to X⊕V, and any intermediate space obtained using ...
Squares from products of integers
(2006)
Notice that 1_2_3_4+1 = 52 , 2_3_4_5+1 = 112 , 3_4_5_6+1 = 192 , . . . . Indeed, it is well known that the product of any four consecutive integers always differs by one from a perfect square. However, a little experimentation ...
The Gaussian cotype of operators from C(K)
(2011)
We show that the canonical embedding C(K) to LΦ(μ) has Gaussian cotype p, where μ is a Radon probability measure on K, and Φ is an Orlicz function equivalent to tp(log t)p/2 for large t.
On the Value Set of n! Modulo a Prime
(2005)
We show that for infinitely many prime numbers p there are at least log log p/ log log log p distinct residue classes modulo p that are not congruent to n! for any integer n.
Lyapunov theorems for Banach spaces
(2011)
We present a spectral mapping theorem for semigroups on any Banach space E. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for E-valued functions. This characterization ...
Congruences and Exponential Sums with the Euler Function
(2004)
We give upper bounds for the number of solutions to congruences with the Euler function φ(n) and with the Carmichael function λ(n). We also give nontrivial bounds for certain exponential sums involving φ(n). Analogous ...
Hardy martingales and Jensen's inequality
(2011)
Hardy martingales were introduced by Garling and used to study analytic functions on the N-dimensional torus TN, where analyticity is defined using a lexicographic order on the dual group ZN. We show how, by using basic ...
The Hardy operator and Boyd indices
(2011)
We give necessary and sufficient conditions for the Hardy operator to be bounded on a rearrangement invariant quasi-Banach space in terms of its Boyd indices.
On the Number of Sparse RSA Exponents
(2002)
An RSA modulus is a product M = pl of two primes p and l. We show that for almost all RSA moduli M, the number of sparse exponents e (which allow for fast RSA encryption) with the property that gcd(e,φ(M)) = 1 (hence RSA ...
Multiresolution Models for Nonstationary Spatial Covariance Functions
(Statistical Modelling, 2002)
Many geophysical and environmental problems depend on estimating a spatial process that has nonstationary structure. A nonstationary model is proposed based on the spatial field being a linear combination of a multiresolution ...
Conditions implying regularity of the three dimensional Navier-Stokes equation
(2011)
We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac ...
Some conjectures about integral means of ∂f and ∂¯f
(2011)
We discuss some conjectural inequalities concerning a problem from the calculus of variations, namely that rank 1 convex functions are quasi-convex. An affirmative answer would also give the best constants for the ...
Almost All Palindromes Are Composite
(2004)
We study the distribution of palindromic numbers (with respect to a fixed base g ≥ 2) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes n ≤ x as x → ∞. Our results ...
Vector-valued weakly analytic measures
(2011)
This paper studies properties of weakly analytic vector-valued measures, an area of study which is relatively unexplored, especially in comparison with scalar-valued measures.
New examples of noncommutative Λ(p) sets
(2003)
In this paper, we introduce a certain combinatorial property Z*(k), which is defined for every integer k ≥ 2, and show that every set E ⊂ Z with the property Z*(k) is necessarily a noncommutative Λ (2k) set. In
particular, ...