JournalsrmiVol. 13, No. 2pp. 411–469

The bilinear Hilbert transform is pointwise finite

  • Michael T. Lacey

    Georgia Institute of Technology, Atlanta, USA
The bilinear Hilbert transform is pointwise finite cover
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Abstract

Let fLf \in L^\infty and gL2g \in L^2 be supported on [0,1]. Then the principal value integral below exists in L1L^1.

p.v.f(x+y)g(xy)dyy.\mathrm {p.v.} \int f(x + y) g (x – y) \frac{dy}{y}.

Cite this article

Michael T. Lacey, The bilinear Hilbert transform is pointwise finite. Rev. Mat. Iberoam. 13 (1997), no. 2, pp. 411–469

DOI 10.4171/RMI/227