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A Martingale Study of the Beurling–Ahlfors Transform inRn

✍ Scribed by Rodrigo Bañuelos; Arthur Lindeman II

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
508 KB
Volume
145
Category
Article
ISSN
0022-1236

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✦ Synopsis

We apply the theory of martingale transforms to study the Beurling Ahlfors transform, S, in dimensions n 2. This operator reveals a rich structure through its representation as a martingale, and we obtain new results concerning the operator norm of S acting on the class of differential forms having L p coefficients. In particular, we show that its norm is independent of the dimension when restricted to k-forms and we present new ``Esse n-type'' norm inequalities related to this martingale structure. Finally, we suggest a purely analytic method to further investigate these norms which up to now has been lacking.

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