Related papers: Linear and bilinear $T(b)$ theorems \`a la Stein

We give a short proof of Stein's universal multiplier theorem, purely by probabilistic methods, thus avoiding any use of harmonic analysis techniques (complex interpolation or transference methods).

This is a companion paper to our previous one, Avatars of Stein's Theorem in the complex setting. In this previous paper, we gave a sufficient condition for an integrable function in the upper-half plane to have an integrable Bergman…

We prove L2 x L2 to weak L1 estimates for some novel bilinear maximal operators of Kakeya and lacunary type thus extending to this setting, the works of Cordoba and of Nagel, Stein and Wainger.

We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear Calder\'{o}n-Zygmund operators as several functions can now…

By a delicate analysis for the Stein's equation associated to the $\alpha$-stable law approximation with $\alpha \in (0,2)$, we prove a quantitative stable central limit theorem in Wasserstein type distance, which generalizes the results in…

In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…

Bilinear restriction estimates have been appeared in work of Bourgain, Klainerman, and Machedon. In this paper we develop the theory of these estimates (together with the analogues for Kakeya estimates). As a consequence we improve the…

We prove a analogous of Stein theorem for rational functions in several variables: we bound the number of reducible fibers by a formula depending on the degree of the fraction.

We completely characterize the class of univariate distributions allowing for a Stein kernel and illustrate our result by means of some concrete distributions. Moreover, we apply our findings to prove a quantitative version of the central…

Certain types of bilinearly defined sets in $\mathbb{R}^n$ exhibit a higher degree of linearity than what is apparent by inspection.

A fundamental result in representation theory is Kostant's theorem which describes the algebra of polynomials on a reductive Lie algebra as a module over its invariants. We prove a quantum analogue of this theorem for the general linear…

In this paper we prove the bilinear analogue of de Leeuw's result for periodic bilinear multipliers and some Jodeit type extension results for bilinear multipliers.

We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…

Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…

Peng, S. (\cite{P08b}) proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein's method.

We obtain a two weight local Tb theorem for any elliptic and gradient elliptic fractional singular integral operator T on the real line, and any pair of locally finite positive Borel measures on the line. This includes the Hilbert transform…

We prove a very general theorem concerning the estimation of the expression $\|T(\frac{a+b}{2}) - \frac{Ta+Tb}{2}\|$ for different kinds of maps $T$ satisfying some general perurbated isometry condition. It can be seen as a quantitative…

A variant of the global $T(1)$ criterion to characterize the bounded Calder\'{o}n--Zygmund operators on BMO($\mathbb{R}^d$) is proved. We apply it to the certain Calder\'on commutators.

We give a self-contained exposition of some mathematical aspects of the Mueller-Stokes formalism. In the first part we review some basic notions of linear algebra and establish a proper notation. In the second part we introduce the…

This article continues and completes our previous work [14] J. Phys. Commun. 2 (2018) 025007. First of all, we present two methods of quantization associated with a linear connection given on a differentiable manifold, one of them being the…