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The class L(log L)α and some lacunary sets

Published online by Cambridge University Press:  09 April 2009

Sanjiv Kumar Gupta
Affiliation:
Department of MathematicsIndian Institute of Technology KanpurKanpur, 208016, India
Shobha Madan
Affiliation:
Department of MathematicsIndian Institute of Technology KanpurKanpur, 208016, India
U. B. Tewari
Affiliation:
Department of MathematicsIndian Institute of Technology KanpurKanpur, 208016, India
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Abstract

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A well-known result of Zygmund states that if f ∈ L (log+L) ½ on the circle group T and E is a Hadamard set of integers, then . In this paper we investigate similar results for the classes on an arbitrary infinite compact abelian group G and Sidon subsets E of the dual Γ. These results are obtained as special cases of more general results concerning a new class of lacunary sets Sαβ, 0 < α ≤ β, where a subset E of Γ is an Sα β set if . We also prove partial results on the distinctness of the Sαβ sets in the index β.

Keywords

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

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