Related papers: Sharp lower bounds for Coulomb energy

The Hamiltonian of the spinless relativistic Coulomb problem combines the standard Coulomb interaction potential with the square-root operator of relativistic kinematics. This Hamiltonian is known to be bounded from below up to some…

Coulomb effects on $\pi^\pm$ and $K^\pm$ spectra in relativistic nuclear collisions are investigated. At collision energies around 1 GeV the ratio of $\pi^-$ to $\pi^+$ is enhanced several times at low transverse momenta but less at…

We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the…

We prove a theorem about elliptic operators with symmetric potential functions, defined on a function space over a closed loop. The result is similar to a known result for a function space on an interval with Dirichlet boundary conditions.…

Let $X$ be a compact K\"ahler manifold with a given ample line bundle $L$. In \cite{Don05}, Donaldson proved that the Calabi energy of a K\"ahler metric in $c_1(L)$ is bounded from below by the supremum of a normalized version of the minus…

We give new lower bounds for $L^p$ estimates of the Schr\"odinger maximal function by generalizing an example of Bourgain.

The Coulomb corrections to the helicity amplitudes of high-energy photon splitting are examined. The consideration is based on the amplitudes obtained exactly in the parameter Z\alpha within the quasiclassical approach valid for small…

We prove uniform $L^p$ estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding resul of [3] in the case of Laplace-- Beltrami operators on…

We prove $L^p \rightarrow L^q$ Fourier restriction estimates for 3-dimensional quadratic surfaces in $\mathbb{R}^5$. Our results are sharp, up to endpoints, for a few classes of surfaces.

In this paper, we study the $L^p(\mathbb{R}^2)$-improving bounds, i.e., $L^p(\mathbb{R}^2)\rightarrow L^q(\mathbb{R}^2)$ estimates, of the maximal function $M_{\gamma}$ along a plane curve $(t,\gamma(t))$, where…

For a smooth $k$-dimensional submanifold $\Sigma$ of a $d$-dimensional compact Riemannian manifold $M$, we extend the $L^p(\Sigma)$ restriction bounds of Burq-G\'erard-Tzvetkov -- originally proved for individual Laplace--Beltrami…

Let $\mathcal{U(\alpha, \lambda)}$, $0<\alpha <1$, $0 < \lambda <1$ be the class of functions $f(z)=z+a_{2}z^{2}+a_{3}z^{3}+\cdots$ satisfying $$\left|\left(\frac{z}{f(z)}\right)^{1+\alpha}f'(z)-1\right|<\lambda$$ in the unit disc ${\mathbb…

Assume that $p\in(1,\infty]$ and $u=P_{h}[\phi]$, where $\phi\in L^{p}(\mathbb{S}^{n-1},\mathbb{R}^{n})$. Then for any $x\in \mathbb{B}^{n}$, we obtain the sharp inequalities $$ |u(x)|\leq…

In this article, we study the fractional spherical maximal function and its lacunary counterpart. We study the necessary and sufficient conditions for $L^p-L^q$ boundedness of both maximal functions. In particular, we prove the restricted…

We prove the $L^p$ bound for the Hilbert transform along variable non-flat curves $(t,u(x)[t]^\alpha+v(x)[t]^\beta)$, where $\alpha$ and $\beta$ satisfy $\alpha\neq \beta,\ \alpha\neq 1,\ \beta\neq 1.$ Comparing with the associated theorem…

Sharp affine fractional $L^p$ Sobolev inequalities for functions on $\mathbb R^n$ are established. The new inequalities are stronger than (and directly imply) the sharp fractional $L^p$ Sobolev inequalities. They are fractional versions of…

Consider a logharmonic polynomial; that is, a product of the form $p(z)\overline{q(z)}$, where $p$, $q$ are holomorphic polynomials. Assume $q$ is linear and denote by $n$ the degree of $p$. It was recently shown in arXiv:2302.04339…

We prove variable coefficient versions of L^p boundedness results on Hilbert transforms and maximal functions along convex curves in the plane.

Let $\{u_\lambda\}$ be a sequence of $L^2$-normalized Laplacian eigenfunctions on a compact two-dimensional smooth Riemanniann manifold $(M,g)$. We seek to get an $L^p$ restriction bounds of the Neumann data $ \lambda^{-1} \partial_\nu…

We give a general lower bound on the frequency of sign changes in the real coefficients of L-functions of the Selberg class. We in particular recover existing results in the cases of GL(2) and GL(3), and obtain new bounds in the case of…