EMBEDDING OF HARDY SPACES INTO WEIGHTED BERGMAN SPACES IN BOUNDED DOMAINS WITH C~2 BOUNDARY

摘要

Let D be a bounded domain in C~n with C~2 boundary. Let H~p(D) be the Hardy space and A~(p,α)(D) be the space of holomorphic functions which are L~p-integrable with respect to the weighted measure dV_α(z) ＝ δ_D(z)~(α-1)dV(z). We obtain some estimates on the mean growth of H~p functions in D. Using these estimates, we can embed the H~p(D) space into A~(q,β)(D) for 0 < p < q < ∞, β > 0 satisfying n/p = (n + β)/q. We also show that the condition of C~2-srnoothness of the boundary of D is an essential condition by giving a counter-example of a convex domain with C~(1,λ) smooth boundary for 0 < λ < 1 which does not satisfy the embedding result.