Certain lacunary cosine series are recurrent
Let the coefficients of a lacunary cosine series be bounded and not square-summable. Then the partial sums of the series are recurrent.
A variant of Hörmander's conditionfor singular integrals
A lower bound in the law of the iterated logarithm for general lacunary series
We prove a lower bound in a law of the iterated logarithm for sums of the form where f satisfies certain conditions and the satisfy the Hadamard gap condition .
A law of the iterated logarithm for general lacunary series
We prove a law of the iterated logarithm for sums of the form where the satisfy a Hadamard gap condition. Here we assume that f is a Dini continuous function on ℝⁿ which has the property that for every cube Q of sidelength 1 with corners in the lattice ℤⁿ, f vanishes on ∂Q and has mean value zero on Q.
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