... α<αD,whereαDis a certain criticalvalue that depends on D (cf. [4]), and assume that ψ : D→C is analytic, bounded awayDana D. Clahane 32. Notation and definitionsAs in [2, page 2], a Hilbert space ᐅ ... pairs of composition opera-tors on the Hardy space,” Journal of Mathematical Analysis and Applications, vol. 305, no. 1, pp.183–196, 2005.[7] J. H. Shapiro and W. Smith, “Hardy spaces that ... Pisa. Classe di Scienze. Serie IV, vol. 21,no. 3, pp. 399–419, 1994.Dana D. Clahane: Department of Mathematics, University of California, Riverside, CA 92521, USAEmail address: dclahane@math.ucr.eduDana...