On the Norm of the Beurling–ahlfors Transformation: Summary of Changes from First Version (12/28/07) to Second Version (2/19/08), and Comments on Dimension 4
نویسنده
چکیده
Sections 12, 13, and 14 in the second version are new, and the numbering of the other sections has changed accordingly. We have also added a comment on weakened martingale conditions (16) in Section 3. In Theorem 1, it is stated now that the result holds not only for p−norms but for Burkholder’s functions u. Of course, the method of proof is that one first obtains the result for the functions u. It seems to be the case that before this paper, while there were results for the p−norm of the Beurling–Ahlfors transformation (involving constants > 1), there were no end results for the functions u, which were only used as intermediate tools.
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تاریخ انتشار 2008