Newtonian Spaces Based on Quasi-Banach Function Lattices
2016 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 119, no 1, 133-160 p.Article in journal (Refereed) Published
In this paper, first-order Sobolev-type spaces on abstract metric measure spaces are defined using the notion of (weak) upper gradients, where the summability of a function and its upper gradient is measured by the "norm" of a quasi-Banach function lattice. This approach gives rise to so-called Newtonian spaces. Tools such as moduli of curve families and Sobolev capacity are developed, which allows us to study basic properties of these spaces. The absolute continuity of Newtonian functions along curves and the completeness of Newtonian spaces in this general setting are established.
Place, publisher, year, edition, pages
Institut for Matematik Aarhus Universitet , 2016. Vol. 119, no 1, 133-160 p.
IdentifiersURN: urn:nbn:se:liu:diva-132102DOI: 10.7146/math.scand.a-24188ISI: 000383815600008OAI: oai:DiVA.org:liu-132102DiVA: diva2:1038351
Funding Agencies|NordForsk Research Network "Analysis and Applications" 2016-10-182016-10-172016-10-26Bibliographically approved