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Composition of quasiconformal mappings and functions in Triebel-Lizorkin spaces


  • Dedicated to Hans Triebel


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