Mathematics, Department of


Date of this Version



Indiana University Mathematics Journal. ©. Vol. 24. No.2 (1974)


Let G be a compact abelian group with dual group Γ. A subset E or Γ is p-Sidon (1 ≤ p < 2) if there is a constant α such that each [?] in C(G) with [?] supported on E satisfies [?]. Hence a set is 1-Sidon if and only if it is Sidon. Moreover a duality argument yields that E is p-Sidon if and only if [?] (E) [?] M(G)[?] [?], where the latter symbol denotes the restrictions of the Fourier-Stieltjes transforms to E and where p' = p/(p - 1). Several of the basic results on p-Sidon sets were independently obtained by Bozejko and Pytlik [1], L-S. Hahn [4], and Edwards and Ross [3]. The article of Edwards and Ross appears to contain all that was known about p-Sidon sets prior to this paper. Here we prove: