Related papers: Sharp capacity estimates for annuli in weighted R^…

We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted $\mathbf{R}^n$ and in metric spaces, primarily under the assumptions of an annular decay property and a Poincar\'e inequality. In particular,…

Using a new method we give elementary estimates for the capacity of non-contractible annuli on cylinders and provide examples, where these inequalities are sharp. Here the lower bound depends only on the area of the annulus. In the case of…

We obtain precise estimates, in terms of the measure of balls, for the Besov capacity of annuli and singletons in complete metric spaces. The spaces are only assumed to be uniformly perfect with respect to the centre of the annuli and…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…

We study model semilinear equations on complete and non-compact weighted Riemannian manifolds with non-negative Bakry-\'Emery Ricci curvature. Our main goal is to classify positive solutions of the equation at the Sobolev-critical exponent,…

In this paper,we count the rational points on the weighted projective spaces defined over number fields w.r.t. ``size''. An asymptotic formula which generalizes the result of Schanuel's ``Heights in number fields'' is obtained. Furthermore,…

We pursue a systematic treatment of the variational capacity on metric spaces and give full proofs of its basic properties. A novelty is that we study it with respect to nonopen sets, which is important for Dirichlet and obstacle problems…

We study sufficient conditions on weight functions under which norm approximations by analytic polynomials are possible. The weights we study include radial, non-radial, and angular weights.

We introduce the notion of weighted singular vectors and weighted uniform exponent with respect to a set of weights. We prove invariance of these exponents for affine subspaces and submanifolds inside those affine subspaces. For certain…

We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$…

We prove genuinely multilinear weighted estimates for singular integrals in product spaces. The estimates complete the qualitative weighted theory in this setting. Such estimates were previously known only in the one-parameter situation.…

We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…

There are many interesting problems about the electrostatic potential of finitely many charges. We consider one of them concerning the intensity of the field, in other words, about the magnitude of the gradient of this potential. We want to…

We prove norm estimates for multilinear fractional integrals acting on weighted and variable Hardy spaces. In the weighted case we develop ideas we used for multilinear singular integrals [7]. For the variable exponent case, a key element…

We obtain sharp estimates for heat kernels and Green's functions on complete noncompact Riemannian manifolds with Euclidean volume growth and nonnegative Ricci curvature. We will then apply these estimates to obtain sharp Moser-Trudinger…

We establish sharp estimates for the $p$-capacity of metric rings with unrelated radii in metric measure spaces equipped with a doubling measure and supporting a Poincar\'e inequality. These estimates play an essential role in the study of…

We study the critical properties of three-dimensional O(N) models, for N=2,3,4. Parameterizing the leading corrections-to-scaling for the $\eta$ exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte…

In the context of radial weights we study the dimension dependence of some weighted inequalities for maximal operators. We study the growth of the $A_1$-constants for radial weights and show the equivalence between the uniform boundedness…

We give asymptotic estimates of the variance of the number of integer points in translated thin annuli in any dimension.

In this paper we prove a quantitative multilinear limited range extrapolation theorem which allows us to extrapolate from weighted estimates that include the cases where some of the exponents are infinite. This extends the recent…