Related papers: Optimal Hardy-weights for the $(p,A)$-Laplacian wi…

Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and $(p_-(L),\, p_+(L))$ be the maximal interval of exponents $q\in[1,\,\infty]$ such that the semigroup…

We give existence and regularity results for solutions of some nonlinear elliptic problems. The equations we deal with are modeled on a problem which involves in its principal part an anisotropic operator, a Hardy-type potential, and a…

We establish optimal L^p bounds for the nontangential maximal function of the gradient of the solution to a second order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the…

We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\infty$ involving the Hardy-Ces\`aro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\le 1$. Moreover, boundedness of the…

We investigate uniqueness of solutions to Schr\"odinger-type elliptic equations posed on infinite graphs. Solutions are assumed to belong to suitable weighted $\ell^p$ spaces where $p\geq 1$ and the weight is related to both the potential…

We proved some optimal Hardy inequalities in RNwhich is closely related to multipolar Schr\"odinger operators with mean-value type potentials, these sharp inequalities imply some multipolar type Heisenberg inequalities. We also obtained…

We present a unified and concise method for establishing L^p Hardy and Rellich inequalities for a broad class of subelliptic operators of divergence type. The approach, based on a fundamental algebraic identity, provides explicit control on…

In this paper the complete solution of the restricted inequalities for supremal operators are given. The boundedness of the composition of supremal operators with the Hardy and Copson operators in weighted Lebesgue spaces are characterized.

Asymptotics of solutions to relativistic fractional elliptic equations with Hardy type potentials is established in this paper. As a consequence, unique continuation properties are obtained.

We construct optimal Hardy weights to subcritical energy functionals $h$ associated with quasilinear Schr\"odinger operators on locally finite graphs. Here, optimality means that the weight $w$ is the largest possible with respect to a…

Let $\mathcal{Q}(\varphi):=\int_\Omega \big(|\nabla \varphi|^p+V|\varphi|^p\big)\dnu$ on $\core$, and assume that $\mathcal{Q}\geq 0$. The aim of the paper is to obtain ''as large as possible" nonnegative (optimal) Hardy-type weight $W$…

Two-weight criteria of various type for the Hardy-Littlewood maximal operator and singular integrals in variable exponent Lebesgue spaces defined on the real line are established.

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…

Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\geq0$) and best constant $\alpha$. We give conditions so that the spectrum of $W^{-1}P$ is $[\alpha,\infty)$. We apply this to…

We establish new optimal reversed Hardy-type inequalities on the cone of decreasing sequences from $\ell^p$-spaces with power weights, as well as estimates between different norms in Lorentz spaces of sequences. Based on these inequalities,…

In this paper we study existence and nonexistence of nonnegative distributional solutions for a class of semilinear fractional elliptic equations involving the Hardy potential.

In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to…

We prove optimal Lieb-Thirring type inequalities for Schr\"odinger and Jacobi operators with complex potentials. Our results bound eigenvalue power sums (Riesz means) by the $L^p$ norm of the potential, where in contrast to the self-adjoint…

In this article we characterize all possible cases that may occur in the relations between the sets of $p$ for which weak type $(p,p)$ and strong type $(p,p)$ inequalities for the Hardy--Littlewood maximal operators, both centered and…

We obtain $L^p(L^q)$ maximal regularity estimates for time dependent second order elliptic operators in divergence form with rough dependencies in the spatial variables.