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MAXIMAL OPERATORS AND HILBERT TRANSFORMS ALONG FLAT CURVES NEAR L1

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  15 December 2009

NEAL BEZ
NEAL BEZ*
Affiliation:
School of Mathematics, The Watson Building, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK (email: bezn@maths.bham.ac.uk)
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Abstract

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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.

Keywords

maximal operatorHilbert transformweak type estimate

MSC classification

Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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

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