REMARKS ON GENERALIZED HILBERT OPERATORS

Abstract Given a regular measure $$\eta \in M([0,1))$$ η ∈ M ( [ 0 , 1 ) and an analytic function $$g\in {\mathcal H}(\mathbb {D})$$ g H D , we define $$H(\eta ,g)(z)=\int _0^1g(tz)d\eta (t)$$ z = ∫ t d study its boundedness from $$X\times Y$$ X × Y into Z where $$X\subset ⊂ $$Y,Z\subset Z are the Hardy spaces. We shall analyze case $$X=L^p([0,1))$$ L p characterize functions such that $$H_g$$ maps $$L^p([0,1))$$ $$H^p(\mathbb $$H_g(\eta )=H(\eta g)$$ .