Related papers: Multilinear paraproducts on Sobolev spaces

Calder\'on-Zygmund operators with noncommuting kernels may fail to be Lp-bounded for $p \neq 2$, even for kernels with good size and smoothness properties. Matrix-valued paraproducts, Fourier multipliers on group vNa's or noncommutative…

Regular polygons are characterized as area-constrained critical points of the perimeter functional with respect to particular families of perturbations in the class of polygons with a fixed number of sides. We also review recent results in…

Let $({\mathcal X}, d, \mu)$ be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition and the non-atomic condition that $\mu(\{x\})=0$ for all $x\in{\mathcal X}$. In this paper,…

We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew-Hermitian differentiation matrix. While a theory of such L2-orthogonal systems is…

In this short note, we extend a local $Tb$ theorem that was proved in \cite{GHO} to a full multilinear local $Tb$ theorem.

Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with a potential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with $\sigma\geq n/2$. The main aim of this paper is to provide necessary and sufficient…

In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…

We prove Bloom type two-weight inequalities for commutators of multilinear singular integral operators including Calder\'on-Zygmund operators and their dyadic counterparts. Such estimates are further extended to a general higher order…

The wave-Sobolev spaces $H^{s,b}$ are $L^2$-based Sobolev spaces on the Minkowski space-time $\R^{1+n}$, with Fourier weights are adapted to the symbol of the d'Alembertian. They are a standard tool in the study of regularity properties of…

In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the…

Let $b$ be a $BMO$-function. It is well-known that the linear commutator $[b, T]$ of a Calder\'on-Zygmund operator $T$ does not, in general, map continuously $H^1(\mathbb R^n)$ into $L^1(\mathbb R^n)$. However, P\'erez showed that if…

It is shown that product BMO of Chang and Fefferman, defined on the product of Euclidean spaces can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of Coifman, Rochberg,…

The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on…

Let $i\in\{1,2\}$ and $X_i$ be a space of homogeneous type in the sense of Coifman and Weiss with the upper dimension $\omega_i$. Also let $\eta_i$ be the smoothness index of the Auscher--Hyt\"onen wavelet function $\psi^{k_i}_{\alpha_i}$…

We consider a class of line operators in d=4, N=2 supersymmetric field theories which leave four supersymmetries unbroken. Such line operators support a new class of BPS states which we call "framed BPS states." These include halo bound…

Let H be a Schrodinger operator with barrier potential on the real line. We define the Besov spaces for H by developing the associated Littlewood-Paley theory. This theory depends on the decay estimates of the spectral operator in the high…

Let (M,\mu) be a sigma-finite measure space. Let (T_t) be a semigroup of positive preserving maps on (M,\mu) with standard assumptions. We prove a H_1-BMO duality theory with assumptions only on T_t. The BMO is defined as spaces of…

In this paper, we will study the boundedness properties of multilinear Calderon--Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

In this paper we present a new characterization of Sobolev spaces on Euclidian spaces ($\mathbb{R}^n$). Our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of…

We prove L^p estimates for a two-dimensional bilinear operator of paraproduct type. This result answers a question posed by Demeter and Thiele in [3].