6533b820fe1ef96bd1279285

RESEARCH PRODUCT

The Besov capacity in metric spaces

Juho Nuutinen

subject

Discrete mathematicsGeneral Mathematics010102 general mathematicsType inequalitykapasiteetti01 natural sciencesMeasure (mathematics)Upper and lower boundsmetriset avaruudetFunctional Analysis (math.FA)Theory basedMathematics - Functional Analysis010101 applied mathematicsMetric spaceBesov spacesContent (measure theory)FOS: Mathematics0101 mathematicsMathematics

description

We study a capacity theory based on a definition of Haj{\l} asz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are $\gamma$-medians, for which we also prove a new version of a Poincar\'e type inequality.

yearjournalcountryeditionlanguage
2016-01-01
http://urn.fi/URN:NBN:fi:jyu-201608023719