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On an equivalence for differentiation bases of dyadic rectangles

Volume 146 / 2017

G. A. Karagulyan, D. A. Karagulyan, M. H. Safaryan Colloquium Mathematicum 146 (2017), 295-307 MSC: 42B08, 42B25. DOI: 10.4064/cm6629-1-2016 Published online: 2 December 2016

Abstract

The paper considers differentiation properties of rare bases of dyadic rectangles corresponding to increasing sequences $\{\nu_k\}$ of integers. We prove that the condition \begin{equation*} \sup_k(\nu_{k+1}-\nu_k) \lt \infty \end{equation*} is necessary and sufficient for such a basis to be equivalent to the full basis of dyadic rectangles.

Authors

  • G. A. KaragulyanInstitute of Mathematics
    Armenian National Academy of Sciences
    Baghramian ave. 24/5
    0019, Yerevan, Armenia
    e-mail
  • D. A. KaragulyanInstitute of Mathematics
    Armenian National Academy of Sciences
    Baghramian ave. 24/5
    0019, Yerevan, Armenia
    e-mail
  • M. H. SafaryanInstitute of Mathematics
    Armenian National Academy of Sciences
    Baghramian ave. 24/5
    0019, Yerevan, Armenia
    e-mail

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