Multiplicative functions with bounded seminorm on the set of shifted primes
In this paper we investigate the connections between the classes Z-o(lN), L*{1N) and La(lP + 1), L " { P + 1) for multiplicative funct ions / . We construct an example of a multiplicative function / € L*(N) such tha t / ^ + 1). If [/(p*")! < Ar® we prove (see Theorem 2) that if / € Li(N) then / € L i ( P + 1) and if / E L'{N) then / € L ' ( P + 1). Under some additional conditions (for example, | / (p ) | > e > 0 for all p) we prove (see Theorem 3) tha t if / e I . i ( P + 1) then / 6 Li {N). AMS 1991 Classification numbers: 11K65, 11N64