A remark on extrapolation of rearrangement operators on dyadic$H^s$, $0< s \le 1$
 作者： Stefan Geiss,  Paul F. X. Müller,  Veronika Pillwein 作者单位： 1Department of Mathematics and Statistics P.O. Box 35 (MaD) FIN-40014 University of Jyväskylä, Finland2Department of Analysis J. Kepler University A-4040 Linz, Austria 刊名： Studia Mathematica, 2005, Vol.171 , pp.196-205 来源数据库： Institute of Mathematics Polish Academy of Sciences DOI： 10.4064/sm171-2-5 原始语种摘要： For an injective map $\tau$ acting on the dyadic subintervals of theunit interval $[0,1)$ we define the rearrangement operator $T_s$,$0< s< 2$, to be the linear extension ofthe map$$\frac{h_I}{|I|^{1/s}} \mapsto\frac{h_{\tau(I)}}{|\tau(I)|^{1/s}},$$where $h_I$ denotes the $L^\infty$-normalized Haar functionsupported on the dyadic interval $I.$We prove the following extrapolation result:If there exists at least one $0< s_0< 2$ such that $T_{s_0}$ is boundedon $H^{s_0}$, then for all $0< s< 2$ the operator $T_{s}$ is boundedon $H^{s}.$

• 校正的　实验
• extrapolation　外推法
• rearrangement　重新配置
• operator　话务员
• injective　内射的
• remark　注意
• extension　延长
• interval　区间
• prove　实验
• normalized　实验