Related papers: Remarks about Hardy inequalities on metric trees
In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, we give necessary and sufficient conditions for the weighted reverse Hardy inequality to be true. The main tool in our proof is a…
In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the…
We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric graphs, several new features appear, such as the existence…
Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities that quantify the extent of the "strictness" of the 1-negative type inequalities for finite metric trees. These…
We present various results concerning the two-weight Hardy's inequality on infinite trees. Our main scope is to survey known characterizations (and proofs) for trace measures, as well as to provide some new ones. Also for some of the known…
In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on H\"older-$\alpha$ domains, where the weights are powers of the distance to the boundary. We obtain results regarding the divergence equation's…
General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are…
In this paper we establish a Hardy inequality for Laplace operators with Robin boundary conditions. For convex domains, in particular, we show explicitly how the corresponding Hardy weight depends on the coefficient of the Robin boundary…
In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…
We consider a family of measures on a $q$-homogeneous tree that decrease exponentially with respect to the distance from the origin. Such measures are doubling with respect to the Gromov distance. We define atomic Hardy and BMO spaces for…
We consider an infinite homogeneous tree $\mathcal V$ endowed with the usual metric $d$ defined on graphs and a weighted measure $\mu$. The metric measure space $(\mathcal V,d,\mu)$ is nondoubling and of exponential growth, hence the…
In this paper we present a new method of proof of Hardy type inequalities for two-dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quantitative lower bound on the best constant in these…
In this note we investigate the multi-parameter Potential Theory on the weighted $d$-tree (Cartesian product of several copies of uniform dyadic tree), which is connected to the discrete models of weighted Dirichlet spaces on the polydisc.…
In this paper we study some weak majorization properties with applications for the trees. A strongly notion of majorization is introduced and Hardy-Littlewood-Polya's inequality is generalized.
[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…
One can describe isomorphism of two compact hyperbolic Riemann surfaces of the same genus by a measure-theoretic property: a chosen isomorphism of their fundamental groups corresponds to a homeomorphism on the boundary of the Poincar\'e…
We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy.…
We provide explicit upper bounds for the eigenvalues of the Laplacian on a finite metric tree subject to standard vertex conditions. The results include estimates depending on the average length of the edges or the diameter. In particular,…
We consider the Dirichlet Laplacian in infinite two-dimensional strips defined as uniform tubular neighbourhoods of curves on ruled surfaces. We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality…
We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well known gap in the spectrum of the Laplacian on the upper half-plane with hyperbolic metric. We make some…