1 results
The class L(log L)α and some lacunary sets
- Part of
-
- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 58 / Issue 3 / June 1995
- Published online by Cambridge University Press:
- 09 April 2009, pp. 387-403
- Print publication:
- June 1995
-
- Article
-
- You have access
- Export citation
-
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.
. In this paper we investigate similar results for the classes 
on an arbitrary infinite compact abelian group 
. We also prove partial results on the distinctness of the 