## Mathematics, Department of

#### Title

#### Date of this Version

1974

#### Citation

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

#### Abstract

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: