Related papers: Quantitative Hardy inequality for magnetic Hamilto…

The Hardy--Littlewood inequality for $m$-homogeneous polynomials on $\ell_{p}$ spaces is valid for $p>m.$ In this note, among other results, we present an optimal version of this inequality for the case $p=m.$ We also show that the optimal…

We study the stability of the Schr\"odinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schr\"odinger equation by the difference of their…

In this paper, we establish a general weighted Hardy type inequality for the $% p-$Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results for different weights. Furthermore, we present…

We consider estimates of Hardy and Littlewood for norms of operators on sequence spaces, and we apply a factorization result of Maurey to obtain improved estimates and simplified proofs for the special case of a positive operator.

We prove a simple sufficient criteria to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second-order differential operator $\Delta_{p}u := \Div(\abs{\nabla u}^{p-2}\nabla u)$. Namely, if $\rho$ is a…

We obtain the sharp factor of the two-sides estimates of the optimal constant in generalized Hardy's inequality with two general Borel measures on $\mathbb{R}$, which generalizes and unifies the known continuous and discrete cases.

We prove multipolar Hardy inequalities on complete Riemannian manifolds, providing various curved counterparts of some Euclidean multipolar inequalities due to Cazacu and Zuazua [Improved multipolar Hardy inequalities, 2013]. We notice that…

The spectrum of the Schr\"odinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any enlargement of the waveguide produces eigenvalues beneath the continuous spectrum. Also if the waveguide is bent…

The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux…

We prove two improved versions of the Hardy-Rellich inequality for the polyharmonic operator $(-\Delta)^m$ involving the distance to the boundary. The first involves an infinite series improvement using logarithmic functions, while the…

We obtain sharp fractional Hardy inequalities for the half-space and for convex domains. We extend the results of Bogdan and Dyda and of Loss and Sloane to the setting of Sobolev-Bregman forms.

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant…

We prove an improved version of Poincar\'e-Hardy inequality in suitable subspaces of the Sobolev space on the hyperbolic space via Bessel pairs. As a consequence, we obtain a new Hardy type inequality with an improved constant (than the…

We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calder\'on-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating…

Let $\Omega$ be an open connected cone in $\mathbb{R}^n$ with vertex at the origin. Assume that the operator $$P_\mu:=-\Delta-\frac{\mu}{\delta_\Omega^2(x)}$$ is {\em subcritical} in $\Omega$, where $\delta_\Omega$ is the distance function…

We prove some Hardy type inequalities related to quasilinear second order degenerate elliptic differential operators L_p(u):=-\nabla_L^*(\abs{\nabla_L u}^{p-2}\nabla_L u). If \phi is a positive weight such that -L_p\phi>= 0, then the Hardy…

We investigate the growth of the polynomial and multilinear Hardy--Littlewood inequalities. Analytical and numerical approaches are performed and, in particular, among other results, we show that a simple application of the best known…

We consider the Hartree equation for infinitely many electrons with a constant external magnetic field. For the system, we show a local well-posedness result when the initial data is the pertubation of a Fermi sea, which is a non-trace…

The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant magnetic field is asymptotic, in norm-resolvent sense, to an effective Hamiltonian which has the form of a multi-particle Schr\"odinger operator with interactions…

Homogenization proposed in [Y.-C Wu and M. \.Zukowski, Phys. Rev. A 85, 022119 (2012)] is a procedure to transform a tight Bell inequality with partial correlations into a full-correlation form that is also tight. In this paper, we check…