Adams inequality on metric measure spaces

DOI10.4171/RMI/575zbMath1186.46031WikidataQ110084955 ScholiaQ110084955MaRDI QIDQ734614

Tero Mäkäläinen

Publication date: 13 October 2009

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1255440067

zbMATH Keywords

Poincaré inequalitytrace inequalityRiesz potentialmetric measure spaceAdams inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Potentials and capacities on other spaces (31C15) Inequalities involving derivatives and differential and integral operators (26D10) Analysis on metric spaces (30L99)

Related Items

The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces ⋮ An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability ⋮ Sharp capacity estimates for annuli in weighted \(\mathbf {R}^n\) and in metric spaces ⋮ Superminimizers and a weak Cartan property for \(p = 1\) in metric spaces ⋮ Extension and trace results for doubling metric measure spaces and their hyperbolic fillings ⋮ Pointwise properties of functions of bounded variation in metric spaces ⋮ Muckenhoupt \(A_p\)-properties of distance functions and applications to Hardy-Sobolev-type inequalities ⋮ The boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous type ⋮ BV capacity on generalized Grushin plane ⋮ The BV-capacity in metric spaces ⋮ Comparisons of relative BV-capacities and Sobolev capacity in metric spaces ⋮ The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Functions of bounded variation on ``good metric spaces
• Characterizations of Sobolev inequalities on metric spaces
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Nonlinear potential theory and weighted Sobolev spaces
• Lectures on analysis on metric spaces
• Fat sets and pointwise boundary estimates for \(p\)-harmonic functions in metric spaces
• Fine properties of sets of finite perimeter in doubling metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Nonlinear potential theory of metric spaces
• Sobolev spaces on an arbitrary metric space
• Sobolev spaces with zero boundary values on metric spaces
• The Poincaré inequality is an open ended condition
• Weakly Differentiable Functions
• Sobolev met Poincaré
• Weighted Norm Inequalities for Fractional Integrals
• The Dirichlet problem for p-harmonic functions on metric spaces
• Sobolev Extensions of Hölder Continuous and Characteristic Functions on Metric Spaces
• Lebesgue points and capacities via boxing inequality in metric spaces
• A trace inequality for generalized potentials
• Regularity of quasi-minimizers on metric spaces
• Harmonic functions on metric spaces

This page was built for publication: Adams inequality on metric measure spaces