Bounded compositions on scaling invariant Besov spaces

2012/09/28 by Koch, Herbert, Koskela, Pekka, Saksman, Eero +1
#30C65 #46E35 #47B33 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1209.6477

Abstract

For 0 < s < 1 < q < ∞, we characterize the homeomorphisms φ: \realⁿ → \realⁿ for which the composition operator f ↦ f ∘ φ is bounded on the homogeneous, scaling invariant Besov space B^s_n/s,q(\realⁿ), where the emphasis is on the case q\not=n/s, left open in the previous literature. We also establish an analogous result for Besov-type function spaces on a wide class of metric measure spaces as well, and make some new remarks considering the scaling invariant Triebel-Lizorkin spaces F^s_n/s,q(\realⁿ) with 0 < s < 1 and 0 < q ≤ ∞.

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