The Bergman Projection and Vector-Valued Hardy Spaces

摘要

Let S~n be the unit sphere in C~n, and let dσ denote the surface area form on S~n normalized so ∫_(S~n) dσ = 1; B_n will denote the unit ball and dv will be the normalized volume form on B_n. We assume familiarity with the invariant Poisson integral and nonisotropic metric d(ζ, η) = |1 — < ζ, η >|~(1/2) used in the study of function theory on S~n; see [R, Chap. 5]. For 0 < p < ∞, H~p(S~n) is the usual space of distributions whose invariant Poisson integrals are holomorphic on B_n and whose admissible maximal functions belong to L~p(dσ); see [R, Chap. 4].