A law of the iterated logarithm for general lacunary series

Volume 126 / 2012

Charles N. Moore, Xiaojing Zhang Colloquium Mathematicum 126 (2012), 95-103 MSC: Primary 42A55; Secondary 60F15. DOI: 10.4064/cm126-1-6

Abstract

We prove a law of the iterated logarithm for sums of the form $\sum_{k=1}^N a_k f(n_k x)$ where the $n_k$ satisfy a Hadamard gap condition. Here we assume that $f$ is a Dini continuous function on $\mathbb R^n$ which has the property that for every cube $Q$ of sidelength 1 with corners in the lattice $\mathbb Z^n$, $f$ vanishes on $\partial Q$ and has mean value zero on $Q.$

Authors

  • Charles N. MooreDepartment of Mathematics
    Kansas State University
    Manhattan, KS 66506, U.S.A.
    e-mail
  • Xiaojing ZhangDepartment of Mathematics
    Kansas State University
    Manhattan, KS 66506, U.S.A.
    e-mail

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