Related papers: Riesz-Schur transforms

The spin-1/2 XXZ Heisenberg chain with two types of boundary terms is considered. For the first type, the Hamiltonian is hermitian but not for the second type which includes the U_{q}[SU(2)] symmetric case. It is shown that for a certain…

We show that the rotation algebras are limit of matrix algebras in a very strong sense of convergence for algebras with additional Lipschitz structure. Our results generalize to higher dimensional noncommutative tori and operator valued…

In this article, we continue the development of the Riemann-Hilbert formalism for studying the asymptotics of Toeplitz+Hankel determinants with non-identical symbols, which we initiated in \cite{GI}. In \cite{GI}, we showed that the…

We prove new sharp $L^p$, logarithmic, and weak-type inequalities for martingales under the assumption of differentially subordination. The $L^p$ estimates are "Fyenman-Kac" type versions of Burkholder's celebrated martingale transform…

We consider bounded linear operators acting on the $\ell_2$ space indexed by the nodes of a homogeneous tree. Using the Cuntz relations between the primitive shifts on the tree, we generalize the notion of the single-scale time-varying…

Let $L=-\Delta + V(x)$ be a Schr\"odinger operator on $\mathbb R^d$, where $V(x)\geq 0$, $V\in L^2_{\rm loc} (\mathbb R^d)$. We give a short proof of dimension free $L^p(\mathbb R^d)$ estimates, $1<p\leq 2$, for the vector of the Riesz…

Let $L_1$ be a nonnegative self-adjoint operator in $L^2({\mathbb R}^n)$ satisfying the Davies-Gaffney estimates and $L_2$ a second order divergence form elliptic operator with complex bounded measurable coefficients. A typical example of…

We prove variation-norm estimates for the Walsh model of the truncated bilinear Hilbert transform, extending related results of Lacey, Thiele, and Demeter. The proof uses analysis on the Walsh phase plane and two new ingredients: (i) a…

By using an $H^{\infty}$ joint functional calculus for strongly commuting operators, we derive a scheme to deduce the $L^p$ boundedness of certain $d$-dimensional Riesz transforms from the $L^p$ boundedness of appropriate one-dimensional…

The Bochner-Riesz multipliers $ B_{\delta }$ on $ \mathbb R ^{n}$ are shown to satisfy a range of sparse bounds, for all $0< \delta < \frac {n-1}2 $. The range of sparse bounds increases to the optimal range, as $ \delta $ increases to the…

In this paper we introduce Stein's square function associated with bilinear Bochner-Riesz means and investigate its $L^p$ boundedness properties. Further, we discuss several applications of the square function in the context of bilinear…

Let $E\subset \mathbb{R}^{n+1}$, $n\ge 2$, be a closed, Ahlfors-David regular set of dimension $n$ satisfying the "Riesz Transform bound" $$\sup_{\varepsilon>0}\int_E\left|\int_{\{y\in E:|x-y|>\varepsilon\}}\frac{x-y}{|x-y|^{n+1}} f(y)…

In 2004, Enriquez-Etingof-Marshall suggested a new approach to the Ginzburg-Weinstein linearization theorem for a quasitriangular Lie bialgebra $(\g,r)$. This approach is based on solving a system of PDEs for a gauge transformation between…

In the present work some Jackson Stechkin type direct theorems of trigonometric approximation are proved in Orlicz spaces with weights satisfying some Muckenhoupt's $A_{p}$ condition. To obtain refined version of the Jackson type inequality…

We calculate the determinant of the bilinear form in middle degree of the generic artinian reduction of the Stanley-Reisner ring of an odd-dimensional simplicial sphere. This proves the odd multiplicity conjecture of Papadakis and Petrotou…

Let B be a unital commutative semi-simple Banach algebra. We study endomorphisms of B which are simultaneously Riesz operators. Clearly compact and power compact endomorphisms are Riesz. Several general theorems about Riesz endomorphisms…

In this paper, we prove the boundedness of Riesz transforms $\partial_{j}(-\Delta)^{-1/2}$ ($j=1,2,...,n$) on the Q-type spaces $Q_{\alpha}^{\beta}(\mathbb{R}^{n})$. As an application, we get the well-posedness and regularity of the…

We give an alternative proof of several sharp commutator estimates involving Riesz transforms, Riesz potentials, and fractional Laplacians. Our methods only involve harmonic extensions to the upper half-space, integration by parts, and…

In a recent article, D. Kazhdan and A. Yom Din conjectured the validity of an asymptotic form of Schur's orthogonality for tempered irreducible unitary representations of semisimple groups defined over local fields. In the non-Archimedean…

We prove an endpoint version of the Stein-Tomas restriction theorem, for a general class of measures, and with a strengthened Lorentz space estimate. A similar improvement is obtained for Stein's estimate on oscillatory integrals of…