Finite-rank intermediate Hankel operators on the Bergman space

摘要

LetL2=L2(D,r dr dθ/π)be the Lebesgue space on theopen unit disc and letLa2=L2∩ℋol(D)be the Bergmanspace. LetPbe the orthogonal projection ofL2ontoLa2and letQbe the orthogonal projection ontoL¯a,02={g∈L2;g¯∈La2,   g(0)=0}. ThenI−P≥Q. The big Hankel operator and the smallHankel operator onLa2are defined as: forϕinL∞,Hϕbig(f)=(I−P)(ϕf)andHϕsmall(f)=Q(ϕf)(f∈La2). In this paper, the finite-rank intermediateHankel operators betweenHϕbigandHϕsmallare studied. We are working on themore general space, that is, the weighted Bergman space.