Forelli-Rudin type operators on the space Lp,q,s(B) and some applications

Abstract

Let φ be a holomorphic automorphism on the unit ball B of Cn, λ and τ be two real numbers. In this paper, we investigate the conditions such that Forelli-Rudin type operators Tλ,τCφ and |T|λ,τCφ are bounded on Lp,q,s(B) for p≥1 or from Hp,q,s(B) to Lp,q,s(B) for p>0. As some applications of |T|λ,τCφ, we give several characterizations for functions in Fp,q,s(B), and prove that Hp,q,s(B) is an automorphism invariant space.