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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 278 - Analysis Colloquium
Xiaochun Li
UCLA
The Hilbert transform along $C^{1+epsilon}$ vector fields
Abstract:
Let $v$ be a vector field from ${mathbb R}^2$ to the unit circle ${mathbb S}^1$. We study the operator $$ H_vf(x)= p.v. int_{-1}^{1}f(x-tv(x))frac{dt}{t},.$$ We prove that if the vector field $v$ has $1+epsilon$ derivatives, then $H_v$ extends to a bounded map from $L^2$ into itself.
Host: Peter Ebenfelt
February 3, 2004
9:00 AM
AP&M 6438
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