相关论文: On a variant of Tartar's first commutation lemma

Consider a partial flag variety $X$ which is not a grassmaninan. Consider also its cohomology ring ${\rm H}^*(X,\ZZ)$ endowed with the base formed by the Poincar\'e dual classes of the Schubert varieties. In \cite{Richmond:recursion}, E.…

We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.

We develop a new approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the…

Let $I_{\alpha}$ be the linear and $\mathcal{I}_{\alpha}$ be the bilinear fractional integral operators. In the linear setting, it is known that the two-weight inequality holds for the first order commutators of $I_{\alpha}$. But the method…

We study non-trivial deformations of the natural action of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbbR^{1|1}$ of th espace of symbols. We calculate obstructions for integrability…

Alternating sign matrices are known to be equinumerous with descending plane partitions, totally symmetric self-complementary plane partitions and alternating sign triangles, but no bijective proof for any of these equivalences has been…

We prove the existence and uniqueness of a *projectively equivariant symbol map*, which is an isomorphism between the space of bidifferential operators acting on tensor densities over $R^n$ and that of their symbols, when both are…

In a previous paper, the second author defined integer-valued functions delta_n on the first cohomology of a 3-manifold, generalizing McMullen's Alexander norm. It was shown that these functions give lower bounds on the Thurston norm. In…

We consider first order linear operators commuting with the operator appearing in the linearized equation of motion of Rarita-Schwinger fields which comes directly from the action. First we consider a simplified operator giving an equation…

A new tautological equation of $\Mbar_{3,1}$ in codimension 3 is derived and proved, using the invariance condition explained in earlier works.

We show that one-dimensional superspace is isomorphic to a non-trivial but consistent limit as $q\to-1$ of the braided line. Supersymmetry is identified as translational invariance along this line. The supertranslation generator and…

We prove that pseudo-differential operators with symbols in the class $S_{1,\delta}^0$ ($0<\delta<1$) are not always bounded on the modulation space $M^{p,q}$ ($q\neq2$).

Let us consider the set S^A(\R^n) of rapidly decreasing functions G:\R^n \to A, where A is a separable C^*-algebra. We prove a version of the Calder\'on-Vaillancourt theorem for pseudodifferential operators acting on S^A(\R^n) whose symbol…

Let $\tau$ denote the divisor function, and $f$ be any multiplicative function that satisfies some mild hypotheses. We establish the asymptotic formula or non-trivial upper bound for the shifted convolution sum $\sum_{n \leq…

Let n>=3 be an odd integer. For any integer a prime to n, define the permutation gamma_{a,n} of {1,...,(n-1)/2} by gamma_{a,n}(x)=n-\dec{ax}_n if {ax}_n>=(n+1)/2, and {ax}_n if {ax}_n<=(n-1)/2, where {x}_n denotes the least nonnegative…

We prove a H\"{o}rmander type multiplier theorem for multilinear Fourier multipiers with multiple weights. We also give weighted estimates for their commutators with vector $BMO$ functions.

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 examinate, formalize and extend the reasoning behind the Cantor's first diagonal argument, obtaining a simple closed-form expression for a bijection between $\mathbb{N}^k$ and $\mathbb{N}$.

Let $\sigma(x,\xi) $ be a sufficiently regular function defined on $R^d \times R^d.$ The pseudo-differential operator with symbol $\sigma$ is defined on the Schwartz class by the formula: \[f\to\sigma f(x)=\int_{R^d} \sigma(x,\xi)…

Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally…