Related papers: Cwikel estimates revisited

In this paper we study the bicomplex version of weighted Hardy spaces. Further, we describe reproducing kernels for the bicomplex weighted Hardy spaces. In particular, we generalize some results which holds for the classical weighted Hardy…

The classical unified theory of Weyl is revisited. The possibility of stable extended electron model in the Einstein-Weyl space is suggested.

The goal of this note is to give, at least for a restricted range of indices, a short proof of homogeneous commutator estimates for fractional derivatives of a product, using classical tools. Both $L^{p}$ and weighted $L^{p}$ estimates can…

This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…

We propose a modification of the three-manifold invariant based on the use of Euclidean metric values ascribed to the elements of manifold triangulation. We thus obtain a nontrivial invariant that can, in particular, distinguish…

This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems

In this paper, we establish a local smoothing estimate on two-dimensional quantum Euclidean space. This is the noncommutative analogue of the one due to Mockenhaupt$-$Seeger$-$Sogge \cite{MSS}. As an application and simultaneously one…

We prove a priori interior $C^{2,\alpha}$ estimates for solutions of fully nonlinear elliptic equations of twisted type. For example, our estimates apply to equations of the type convex + concave. These results are particularly well suited…

We show that the Euclidean Snyder non-commutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying deformed Heisenberg algebras. Considering…

In this note we obtain semiclassical resolvent estimates for non-trapping long range perturbations of the Laplacian on asymptotically Euclidean manifolds. Our proof is based on a positive commutator argument which differs from Mourre-type…

This paper is a continuation of the papers [2,3,4,5,6]. In this paper the osculating spaces of arbitrary order of a manifold embedded in Euclidean space are considered. A better estimation of their dimensions as well as the description of…

We prove genuinely multilinear weighted estimates for singular integrals in product spaces. The estimates complete the qualitative weighted theory in this setting. Such estimates were previously known only in the one-parameter situation.…

The analog of the Schauder inequality for closed surfaces in Euclidean spaces is obtained in this article.

In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…

Locally noncommutative spacetimes provide a refined notion of noncommutative spacetimes where the noncommutativity is present only for small distances. Here we discuss a non-perturbative approach based on Rieffel's strict deformation…

We prove global Strichartz estimates (with spectral cutoff on the low frequencies) for non trapping metric perturbations of the Schroedinger equation, posed on the Euclidean space.

We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the case of the line, there exists a (unique) "exotic" isometric flow.…

We mainly consider the general Caffarelli-Kohn-Nirenberg inequality in the Euclidean and Riemannian setting. In both cases, our proof relies mostly on a new parameter s conveniently introduced, see (2.7).

We establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the independent variables.

This paper develops a Carleman type estimate for immersed surface in Euclidean space at infinity. With this estimate, we obtain an unique continuation property for harmonic functions on immersed surfaces vanishing at infinity, which leads…