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On the partial sums of Walsh–Fourier series

Volume 141 / 2015

George Tephnadze Colloquium Mathematicum 141 (2015), 227-242 MSC: Primary 42C10. DOI: 10.4064/cm141-2-7

Abstract

We investigate convergence and divergence of specific subsequences of partial sums with respect to the Walsh system on martingale Hardy spaces. By using these results we obtain a relationship of the ratio of convergence of the partial sums of the Walsh series and the modulus of continuity of the martingale. These conditions are in a sense necessary and sufficient.

Authors

  • George TephnadzeDepartment of Mathematics
    Faculty of Exact and Natural Sciences
    Tbilisi State University
    Chavchavadze St. 1
    Tbilisi 0128, Georgia
    and
    Department of Engineering Sciences and Mathematics
    Luleå University of Technology
    SE-971 87 Luleå, Sweden
    e-mail

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