A T(1) Theorem for Fractional Sobolev Spaces on Domains

© 2017, Mathematica Josephina, Inc. Given any uniform domain Ω , the Triebel–Lizorkin space Fp,qs(Ω) with 0 < s< 1 and 1 < p, q< ∞ can be equipped with a norm in terms of first-order differences restricted to pairs of points whose distance is comparable to their distance to the boundary. Using this new characterization, we prove a T(1)-theorem for fractional Sobolev spaces with 0 < s< 1 for any uniform domain and for a large family of Calderón–Zygmund operators in any ambient space Rd as long as sp> d.