6533b7d9fe1ef96bd126ce3b

RESEARCH PRODUCT

Pointwise characterizations of Besov and Triebel–Lizorkin spaces and quasiconformal mappings

Dachun YangYuan ZhouPekka Koskela

subject

Mathematics(all)Quasiconformal mappingPure mathematicsGeneral MathematicsGrand Besov spaceMetric measure spaceTriebel–Lizorkin spaceCharacterization (mathematics)Space (mathematics)Triebel–Lizorkin space01 natural sciencesMeasure (mathematics)Quasisymmetric mappingMorphism0101 mathematicsBesov spaceHajłasz–Besov spaceMathematicsPointwiseta111010102 general mathematicsGrand Triebel–Lizorkin spaceQuasiconformal mappingHajłasz–Triebel–Lizorkin space010101 applied mathematicsBesov spaceFractional Hajłasz gradient

description

Abstract In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces B ˙ p , q s and Triebel–Lizorkin spaces F ˙ p , q s for all s ∈ ( 0 , 1 ) and p , q ∈ ( n / ( n + s ) , ∞ ] , both in R n and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve F ˙ n / s , q s on R n for all s ∈ ( 0 , 1 ) and q ∈ ( n / ( n + s ) , ∞ ] . A metric measure space version of the above morphism property is also established.

yearjournalcountryeditionlanguage
2011-03-01Advances in Mathematics
https://doi.org/10.1016/j.aim.2010.10.020