A remark on extrapolation of rearrangement operators on dyadic$H^s$, $0< s \le 1$
作者: Stefan GeissPaul F. X. MüllerVeronika Pillwein
作者单位: 1Department of Mathematics and Statistics P.O. Box 35 (MaD) FIN-40014 University of Jyväskylä, Finland
2Department 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 $H^{s}.$
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  • 校正的 实验
  • dyadic 二重的
  • 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