Related papers: The Marcinkiewicz multiplier theorem revisited

We present a new proof of a Finslerian version of Beltrami's theorem (1865) which works also in dimension 2.

In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…

The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…

We use Oberlin, Nazarov, and Thiele's Multi-Frequency Calder\'{o}n-Zygmund decomposition to lower estimates on maximal multipliers in $L^p$. We also improve on classical multiplier results of Coifman, Rubio de Francia, and Semmes.

Resolving the details of an object from coarse-scale measurements is a classical problem in applied mathematics. This problem is usually formulated as extrapolating the Fourier transform of the object from a bounded region to the entire…

We present a class of permutations for which the number of distinctly ordered subsequences of each permutation approaches an almost optimal value as the length of the permutation grows to infinity.

We introduce the dual isoperimetrix which solves the isoperimetric problem in the dual Brunn-Minkowski theory. We then show how the dual isoperimetrix is related to the isoperimetrix from the Brunn-Minkowski theory.

Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in…

We review some recent results on $K$-theory of perfection of commutative $\mF_p$-algebras and provide an alternative proof.

In this article we use Littlewood-Paley-Stein theory to prove two versions of Dunkl multiplier theorem when the multiplier $ m $ satisfies a modified H\"ormander condition. When $ m $ is radial we give a simple proof of a known result. For…

New sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper.

Given an Orlicz space $ L^2 \subseteq X \subseteq L^1$ on $[0,1]$, with submultiplicative Young function ${\mathrm{Y}_X}$, we fully characterize the closed null sets $\Xi$ of the real line with the property that H\"ormander-Mihlin or…

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

In this paper, we prove that optimally solving an $n \times n \times n$ Rubik's Cube is NP-complete by reducing from the Hamiltonian Cycle problem in square grid graphs. This improves the previous result that optimally solving an $n \times…

This letter casts the problem of optimum discrete beamforming as the computation of the Minkowski sum of convex polygons, which is itself a convex polygon. The number of vertices of the latter is at most the sum of the number of vertices of…

We motivate and then prove a generalized pythagorean theorem for parallelepipeds in Euclidean space.

We show a new large sieve version of the Brun-Titchmarsh theorem.

We present an alternative proof of the Alexander-Hirschowitz Theorem in dimension 3 using degenerations of toric varieties.

An technically interesting proof of a known theorem.

The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.