Equivalence of sparse and Carleson coefficients for general sets

Timo S. Hänninen University of Helsinki

Classical Analysis and ODEs mathscidoc:1912.43019

Arkiv for Matematik, 56, (2), 333 – 339, 2018
We show that sparse and Carleson coefficients are equivalent for every countable collection of Borel sets and hence, in particular, for dyadic rectangles, the case relevant to the theory of bi-parameter singular integrals. The key observation is that a dual refomulation by I. E. Verbitsky for Carleson coefficients over dyadic cubes holds also for Carleson coefficients over general sets.
Carleson coefficients, sparse coefficients
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  title={Equivalence of sparse and Carleson coefficients for general sets},
  author={Timo S. Hänninen},
  booktitle={Arkiv for Matematik},
  pages={333 – 339},
Timo S. Hänninen. Equivalence of sparse and Carleson coefficients for general sets. 2018. Vol. 56. In Arkiv for Matematik. pp.333 – 339. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204103319823633575.
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