Related papers: Multiparameter Riesz Commutators
Manifold-valued parameters routinely arise in modern statistical applications such as in medical imaging, robotics, and computer vision, to name a few. While traditional Bayesian approaches are applicable to such settings by considering an…
We show a perturbation result for the boundedness of the Riesz transform : if $M$ and $M_0$ are complete Riemannian manifolds satisfying a Sobolev inequality of dimension $n$, which are isometric outside a compact set, and if the Riesz…
We present a coherent approach to recurrence and transience, starting from a version of the Riesz decomposition theorem for superharmonic elements. Our approach allows straightforward proofs of some known results, entails new theorems, and…
We study asymptotic shape optimization for Riesz means of Robin Laplacian eigenvalues among cuboids of fixed measure. Our focus is the regime where the Robin parameter is proportional to the square root of the spectral parameter defining…
We show how to perform integrals over products of distributions in coordinate space such as to reproduce the results of momentum space Feynman integrals in dimensional regularization. This ensures the invariance of path integrals under…
In this paper we prove that the variation operators associated with the heat semigroup and Riesz transforms related to the Schr\"odinger operator are bounded on the suitable $BMO$ type space.
In this paper, we focus on a class of fractional type integral operators that can be served as extensions of Riesz potential with kernels $$K(x,y)=\frac{\Omega_1(x-A_1 y)}{|x-A_1 y |^{\frac{n}{q_1}}} \cdots \frac{\Omega_m(x-A_m y)}{|x-A_m y…
A general class of weighted multilinear Hardy-Ces\`aro operators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on…
Fix $d\geq 2$, and $s\in (d-1,d)$. We characterize the non-negative locally finite non-atomic Borel measures $\mu$ in $\mathbb{R}^d$ for which the associated $s$-Riesz transform is bounded in $L^2(\mu)$ in terms of the Wolff energy. This…
Commutators of bilinear Calder\'on-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact on appropriate products of weighted Lebesgue spaces.
A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical…
This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.
We introduce a new notion of commutator which depends on a choice of subvariety in any variety of omega-groups. We prove that this notion encompasses Higgins's commutator, Froehlich's central extensions and the Peiffer commutator of…
We develop a comprehensive theory for a general class of multi-parameter function spaces of Besov-Triebel-Lizorkin type, with a matrix weight. We prove the equivalence of different quasi-norms, the identification of function and sequence…
We investigate Fourier multipliers on the compact dual of arbitrary discrete groups. Our main result is a H\"ormander-Mihlin multiplier theorem for finite-dimensional cocycles with optimal smoothness condition. We also find Littlewood-Paley…
The $L^p$-boundedness for $p>2$ of the covariant Riesz transform on differential forms is proved for a class of non-compact weighted Riemannian manifolds under certain curvature and volume growth conditions, which in particular settles a…
The well-known necessary and sufficient criteria for the Riemann hypothesis of M. Riesz and Hardy-Littlewood, based on the order of growth at infinity along the positive real axis of certain entire functions, are here imbedded in a general…
Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we are able to prove the multiplicity one theorem for the Ginzburg-Rallis model over the Vogan packets in the…
We discuss the choice of parameters and report some results for unquenched simulations of the Schroedinger functional with a non-hermitean variant of Luescher's multi-boson algorithm.
We prove new results for multi-parameter singular integrals. For example, we prove that bi-parameter singular integrals in $\mathbb{R}^{n+m}$ satisfying natural $T1$ type conditions map $L^q(\mathbb{R}^n; L^p(\mathbb{R}^m;E))$ to…