Related papers: Lorentz space estimates for vector fields with div…

We prove local refined versions of Hardy's and Rellich's inequalities as well as of uncertainty principles for sums of squares of vector fields on bounded sets of smooth manifolds under certain assumptions on the vector fields. We also give…

We construct the general Lorentz-violating effective field theory in curved spacetime and the corresponding nonrelativistic Hamiltonian in the Earth's gravitational field. Applying this general framework to three types of experiments,…

We prove a bound on the sum of the product of curl-free and divergence-free vector fields. Under appropriate orthonormality conditions our bound scales sublinearly in the number of terms, similar in spirit to Lieb--Thirring inequalities.

We prove the $L^2$ boundedness of the directional Hilbert transform in the plane relative to measurable vector fields which are constant on suitable Lipschitz curves.

We prove that a $IR n+1$-valued vector field on IR n is the sum of the traces of two harmonic gradients, one in each component of $IR n+1 \ IR n$ , and of a $IR n$-valued divergence free vector field. We apply this to the description of…

In this paper, we can obtain curvature estimates for spacelike admissible graphic hypersurfaces in the $(n+1)$-dimensional Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, and through which the existence of spacelike admissible graphic…

We prove a fractional Hardy-type inequality for vector fields over the half space based on a modified fractional semi-norm. A priori, the modified semi-norm is not known to be equivalent to the standard fractional semi-norm and in fact…

This study demonstrates that the common practice of determining spontaneous Lorentz violation via the minimum of a Lagrangian potential is generally incorrect. By analyzing the Hamiltonian structure and constraints of vector fields, we show…

We obtain estimates in Besov, Lizorkin-Triebel and Lorentz spaces of differential forms on R^n in terms of their L^1 norm.

Perturbative expansions of relativistic quantum field theories typically contain ultraviolet divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most…

Let $\Omega$ be a strongly Lipschitz domain of $\reel^n$. Consider an elliptic second order divergence operator $L$ (including a boundary condition on $\partial\Omega$) and define a Hardy space by imposing the non-tangential maximal…

Lorentz covariant generalisations of the notions of supersymmetry, superspace and self-duality are discussed. The essential idea is to extend standard constructions by allowing tangent vectors and coordinates which transform according to…

Curl-measure fields are $p$-integrable vector fields whose distributional curl is a vector-valued Radon measure with finite total variation. They were introduced in arXiv:2509.26465, where, for $p= \infty$, the existence of tangential…

If there is Lorentz symmetry violation in the $t$ quark sector of the standard model, changes to particles' dispersion relations might allow for the existence of stable top-flavored hadrons. Observations of the survival of high-energy…

We prove that if $p>1$ then the divergence of a $L^p$-vectorfield $V$ on a 2-dimensional domain $\Omega$ is the boundary of an integral 1-current, if and only if $V$ can be represented as the rotated gradient $\nabla^\perp u$ for a…

Among those nearly incompressible vector fields ${\bf{v}}:{\mathbb{R}}^n\to{\mathbb{R}}^n$ with $|x|\log|x|$ growth at infinity, we give a pointwise characterization of the ones for which $\operatorname{curl}{\bf{v}}= D{\bf{v}}-D^t{\bf{v}}$…

In the paper, we study the three-dimensional Prandtl equations without any monotonicity condition on the velocity field. We prove that when one tangential component of the velocity field has a single curve of non-degenerate critical points…

We consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space $\mathbb{R}^{3}$. We determine all ruled surfaces and all relative…

The aim of this note is to give the boundedness conditions for Hausdorff operators on Hardy spaces $H^{1}$ with the norm defined via $(1,q)$ atoms over homogeneous spaces of Lie groups with doubling property and to apply results we obtain…

We consider here the possibility of quantum gravity induced violation of Lorentz symmetry (LV). Even if suppressed by the inverse Planck mass such LV can be tested by current experiments and astrophysical observations. We review the…