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MAXIMAL OPERATORS AND HILBERT TRANSFORMS ALONG FLAT CURVES NEAR L1
Published online by Cambridge University Press: 15 December 2009
Abstract
For a class of convex curves in ℝd we prove that the corresponding maximal operator and Hilbert transform are of weak type Llog L. The point of interest here is that this class admits curves which are infinitely flat at the origin. We also prove an analogous weak type result for a class of nonconvex hypersurfaces.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 87 , Issue 3 , December 2009 , pp. 311 - 323
- Copyright
- Copyright © Australian Mathematical Publishing Association, Inc. 2009