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arXiv · 1201.3513

A note on dyadic coverings and nondoubling Calderón-Zygmund theory

Jose M. Conde
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Abstract

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) \le 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 Calderón-Zygmund decomposition which avoids Besicovitch type coverings in Tolsa's decomposition. We also use a recent result of Hytönen and Kairema to extend our dyadic nondoubling decomposition to the more general setting of upper doubling metric spaces.

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Jose M. Conde. 2012-03-15. A note on dyadic coverings and nondoubling Calderón-Zygmund theory. https://arxiv.org/abs/1201.3513

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