Related papers: The Marcinkiewicz multiplier theorem revisited

We give a parametrization with perfect sets of the abstract Ellentuck theorem. The main tool for achieving this goal is a sort of parametrization of an abstract version of the Nash-Williams theorem. As corollaries, we obtain some known…

We present a creative reimagining of Zolotarev's classical proof of the Law of Quadratic Reciprocity.

We prove an inequality on positive real numbers, that looks like a reverse to the well-known Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal.

In this article, we provide a multilinear version of the H\"ormander multiplier theorem with a Lorentz-Sobolev space condition. The work is motivated by the recent result of the first author and Slav\'ikov\'a where an analogous version of…

New cases of the multiplicity conjecture are considered.

This paper is concerned with an optimization problem governed by the Kantorovich optimal transportation problem. This gives rise to a bilevel optimization problem, which can be reformulated as a mathematical problem with complementarity…

Several exact expansions as well as lower and upperbounds of the Kermack and McKendrick SIR equations are presented.

We give several new applications of our theorem on the existence of multiplicity of graded families of ideals as a limit, including a very general Minkowski type inequality for graded families of ideals, a very general formula for existence…

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to…

In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We develop a special multilinear complex interpolation theorem that allows us to prove an optimal version of the bilinear H\"ormander multiplier theorem concerning symbols that lie in the Sobolev space $L^r_s(\mathbb R^{2n})$, $2\le…

We study the maximum multiplicity $\mathcal{M}(k,n)$ of a simple transposition $s_k=(k \: k+1)$ in a reduced word for the longest permutation $w_0=n \: n-1 \: \cdots \: 2 \: 1$, a problem closely related to much previous work on sorting…

In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.

We improve constants in the Rademacher-Menchov inequality.

In this paper we prove some interpolation theorems for the multipliers of the Cauchy- Stiltjes type integrals

We verify a conjecture of Lutwak, Yang, Zhang about the equality case in the Orlicz-Petty projection inequality, and provide an essentially optimal stability version.

We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.

We prove an isoperimetric-type inequality for maximal, spacelike submanifold in the Minkowski space. The argument is based on the recent work of Brendle.