TY - JOUR
T1 - BMO estimates for the H∞ (Bn) Corona problem
AU - Costea, Şerban
AU - Sawyer, Eric T.
AU - Wick, Brett D.
PY - 2010/6/1
Y1 - 2010/6/1
N2 - We study the H∞ (Bn) Corona problem ∑j = 1N fj gj = 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∞ ṡ 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 over(∂, -)-problems and to exploit the connection between BMO functions and Carleson measures for H2 (Bn). Key to this is the exact structure of the kernels that solve the over(∂, -) 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.
AB - We study the H∞ (Bn) Corona problem ∑j = 1N fj gj = 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∞ ṡ 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 over(∂, -)-problems and to exploit the connection between BMO functions and Carleson measures for H2 (Bn). Key to this is the exact structure of the kernels that solve the over(∂, -) 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.
KW - Besov-Sobolev spaces
KW - BMO
KW - Carleson measures
KW - Corona problem
UR - https://www.scopus.com/pages/publications/77949568694
U2 - 10.1016/j.jfa.2009.12.015
DO - 10.1016/j.jfa.2009.12.015
M3 - Article
AN - SCOPUS:77949568694
SN - 0022-1236
VL - 258
SP - 3818
EP - 3840
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 11
ER -