科研之友
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摘要
We construct a family of n + 1 dyadic filtrations in R-n, so that every Euclidean ball B is contained in some cube Q of our family satisfying diam(Q) %26lt;= c(n)diam(B) for some dimensional constant c(n). Our dyadic covering is optimal on the number of filtrations and improves previous results of Christ and Garnett/Jones by extending a construction of Mei for the n-torus. Based on this covering and motivated by applications to matrix-valued functions, we provide a dyadic nondoubling Calderon-Zygmund decomposition which avoids Besicovitch type coverings in Tolsa%26apos;s decomposition. We also use a recent result of Hytonen and Kairema to extend our dyadic nondoubling decomposition to the more general setting of upper doubling metric spaces.
- 出版日期2013-1-15
