Resistance Conditions and Applications

• Autorzy: Juha Kinnunen , Pilar Silvestre
• Języki publikacji: EN

Abstrakty

EN

This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with a doubling measure. These conditions are weaker than the usually assumed Poincaré inequality, but however, they are sufficiently strong to imply several useful results in analysis on metric measure spaces. We show that under a perimeter resistance condition, the capacity of order one and the Hausdorff content of codimension one are comparable. Moreover, we have connections to the Sobolev inequality for compactly supported Lipschitz functions on balls as well as capacitary strong type estimates for the Hardy-Littlewood maximal function. We also consider extensions to Sobolev type inequalities with two different measures and Lorentz type estimates.

Słowa kluczowe

EN

Metric measure space; resistance condition; Poincaré inequality; Hausdorff content of codimension one; Hardy-Littlewood maximal function; Sobolev type inequalities

Kategorie tematyczne

• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 31C45: Other generalizations (nonlinear potential theory, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2013
• Tom: 1
• Strony: 276-294

Daty

otrzymano

2013-03-28

zaakceptowano

2013-10-04

online

2013-10-25

Twórcy

autor

Juha Kinnunen

• Department of Mathematics, Aalto University,
  FI-00076 Aalto, Finland

autor

Pilar Silvestre

• Department of Mathematics, Aalto University,
  FI-00076 Aalto, Finland

Bibliografia

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Identyfikatory

DOI

10.2478/agms-2013-0007