Hilbert transforms and maximal functions along variable flat curves

Jonathan Bennett

Type: Article

Publication Date: 2002-07-16

Citations: 20

DOI: https://doi.org/10.1090/s0002-9947-02-03087-8

Abstract

We study certain Hilbert transforms and maximal functions along variable flat curves in the plane. We obtain their $L^{2}(\mathbb {R}^{2})$ boundedness by considering the oscillatory singular integrals which arise from an application of a partial Fourier transform.

Locations

Transactions of the American Mathematical Society - View - PDF

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