A T(1) Theorem for Fractional Sobolev Spaces on Domains
A T(1) Theorem for Fractional Sobolev Spaces on Domains
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DOI：
10.1007/s12220-017-9770-y
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发表时间：
2017-07-01
影响因子：
1.1
通讯作者：
Saksman, Eero
中科院分区：
文献类型：
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作者：
Prats, Marti;Saksman, Eero
给定任何一致域Ω，Triebel-Lizorkin空间F-p（s），（q）（Ω）（0 < s < 1且1 < p，q <无穷大）可以配备一个一阶差范数，该范数仅限于距离与其到边界的距离相当的点对。利用这个新的刻画，我们证明了0 <sd的分数Sobolev空间的一个T（1）-定理< 1 for any uniform domain and for a large family of Calderon-Zygmund operators in any ambient space R-d as long as sp >.
Given any uniform domain Omega, the Triebel-Lizorkin space F-p(s),(q)( Omega) with 0 < s < 1 and 1 < p, q < infinity 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 Calderon-Zygmund operators in any ambient space R-d as long as sp > d.