MAXIMAL OPERATORS AND HILBERT TRANSFORMS ALONG FLAT CURVES NEAR <i>L</i><sup>1</sup>

Neal Bez

Type: Article

Publication Date: 2009-12-01

Citations: 0

DOI: https://doi.org/10.1017/s1446788709000111

Abstract

Abstract For a class of convex curves in ℝ d we prove that the corresponding maximal operator and Hilbert transform are of weak type L log 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.

Locations

Journal of the Australian Mathematical Society - View - PDF
University of Birmingham Research Portal (University of Birmingham) - View - PDF

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