ar X iv : 0 90 5 . 14 76 v 1 [ m at h . C A ] 1 0 M ay 2 00 9 BMO ESTIMATES FOR THE H ∞ ( B n ) CORONA PROBLEM
نویسندگان
چکیده
We study the H(Bn) Corona problem PN j=1 fjgj = h and show it is always possible to find solutions f that belong to BMOA(Bn) for any n > 1, including infinitely many generators N . This theorem improves upon both a 2000 result of Andersson and Carlsson and the classical 1977 result of Varopoulos. The former result obtains solutions for strictly pseudoconvex domains in the larger space H ·BMOA with N = ∞, while the latter result obtains BMOA(Bn) solutions for just N = 2 generators with h = 1. Our method of proof is to solve ∂-problems and to exploit the connection between BMO functions and Carleson measures for H(Bn). Key to this is the exact structure of the kernels that solve the ∂ equation for (0, q) forms, as well as new estimates for iterates of these operators. A generalization to multiplier algebras of Besov-Sobolev spaces is also given.
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تاریخ انتشار 2009