Related papers: Sur les estimations du type sup+inf et sup*inf

In this paper we extend a Calderon-Zygmund commutator-type estimate. This estimate enables us to prove an embedding result concerning weighted function spaces.

We give explicit estimates for the Stirling numbers of the second kind $S(n,m)$. With a few exceptions, such estimates are asymptotically sharp. The form of these estimates varies according to $m$ lying in the central or non-central regions…

We obtain weak type (1,1) estimates for the inverses of truncated discrete rough Hilbert transform. We include an ex- ample showing that our result is sharp. One of the ingredients of the proof are regularity estimates for convolution of…

We prove, in a unified way, $r$-variational estimates, $r>2$, on $\ell^{s}(\mathbb{Z})$ spaces, $s \in (1, \infty)$, for averages and truncated singular integrals along the set of prime numbers.

Another approach to constructing an upper bound for the Riemann-Farey sum is described.

In this article, we obtain certain estimate for the shifted convolution sum involving the Fourier coefficients of half-integral weight cusp forms.

We connect Dedekind sums and some formulas for numerical semigroups.

New cases of the multiplicity conjecture are considered.

We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.

We survey the classical results on the prime number theorem

We give some theoretical and computational results on "random" harmonic sums with prime numbers, and more generally, for integers with a fixed number of prime factors.

We obtain non-trivial lower estimate for the qoutient of two subsets of the interval.

The authors use steepest descent ideas to obtain a priori $L^p$ estimates for solutions of Riemann-Hilbert Problems. Such estimates play a crucial role, in particular, in analyzing the long-time behavior of solutions of the perturbed…

We summarize results concerning the Bernstein property of differential equations.

We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.

We give some comments on W.M. Schmidt's theorem on Diophantine approximations with positive integers and our recent results on the topic.

We analyze different types of simulations that applied researchers can use to assess whether their inference methods reliably control false-positive rates. We show that different assessments involve trade-offs, varying in the types of…

We study a Szemer\'edi-Trotter type theorem in finite fields. We then use this theorem to obtain an improved sum-product estimate in finite fields.

We extend previous semi-classical resolvent estimates for real-valued compactly supported $L^\infty$ potentials to non-compactly supported $L^\infty$ potentials.

We prove $q$-variation estimates, $q>2$, on $\ell^{p}$ spaces for averages along primes (with $1<p<\infty$) and polynomials (with $\big| \frac1p - \frac12 \big| < \frac{1}{2(d+1)}$, where $d$ is the degree of the polynomial). This improves…