TY - JOUR
T1 - A T(1) Theorem for Fractional Sobolev Spaces on Domains
AU - Prats, Martí
AU - Saksman, Eero
PY - 2017/7/1
Y1 - 2017/7/1
N2 - © 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.
AB - © 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.
KW - Besov
KW - Calderón–Zygmund operators
KW - First-order differences
KW - Fourier multipliers
KW - Sobolev
KW - Triebel–Lizorkin
UR - https://www.scopus.com/pages/publications/85014149043
U2 - 10.1007/s12220-017-9770-y
DO - 10.1007/s12220-017-9770-y
M3 - Article
SN - 1050-6926
VL - 27
SP - 2490
EP - 2538
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 3
ER -