6533b828fe1ef96bd12882dc

RESEARCH PRODUCT

Composition of quasiconformal mappings and functions in Triebel-Lizorkin spaces

Pekka KoskelaStanislav Hencl

subject

CombinatoricsGeneral MathematicsBounded functionMathematical analysisComposition (combinatorics)Value (mathematics)Mathematics

description

Let α > 0 and p ∈ [1, ∞) satisfy αp ≤ n. Suppose that f: Rn Rn is a K-quasiconformal mapping and let u ∈ Wα, p(Rn) have compact support. We find an optimal value of β = β(α, K, n) such that u○f ∈ Wβ, p(Rn). We also give an answer to the analogous problem where we moreover assume that u is bounded.

https://doi.org/10.1002/mana.201100130