LITTLEWOOD’S INEQUALITY FOR p−BIMEASURES

A new restructured Hardy-Littlewood's inequality

In this paper, we reconstruct the Hardy-Littlewood’s inequality byusing the method of the weight coefficient and the technic of real analysis includinga best constant factor. An open problem is raised.

Trigonometric Polynomials with Many Real Zeros and a Littlewood-type Problem

We examine the size of a real trigonometric polynomial of degree at most n having at least k zeros in K := R (mod 2π) (counting multiplicities). This result is then used to give a new proof of a theorem of Littlewood concerning flatness of unimodular trigonometric polynomials. Our proof is shorter and simpler than Littlewood’s. Moreover our constant is explicit in contrast to Littlewood’s appro...

Invariant Measures and the Set of Exceptions to Littlewood’s Conjecture

We classify the measures on SL(k,R)/SL(k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood’s conjecture has Hausdorff dimension zero.

On the asymptotic analysis of Littlewood’s reliability model for modular software

2 4 Ju n 20 05 MEASURE RIGIDITY AND p - ADIC LITTLEWOOD - TYPE PROBLEMS

The paper investigates various p-adic versions of Littlewood’s conjecture, generalizing a set-up considered recently by de Mathan and Teulié. In many cases it is shown that the sets of exceptions to these conjectures have Hausdorff dimension zero. The proof follows the measure ridigity approach of Einsiedler, Katok and Lindenstrauss.