Revista Matemática Iberoamericana


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Volume 13, Issue 2, 1997, pp. 411–469
DOI: 10.4171/RMI/227

The bilinear Hilbert transform is pointwise finite

Michael T. Lacey[1]

(1) School of Mathematics, Georgia Institute of Technology, GA 30332-0160, ATLANTA, UNITED STATES

Let $f \in L^\infty$ and $g \in L^2$ be supported on [0,1]. Then the principal value integral below exists in $L^1$. $$\mathrm {p.v.} \int f(x + y) g (x – y) \frac{dy}{y}.$$

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Lacey Michael: The bilinear Hilbert transform is pointwise finite. Rev. Mat. Iberoamericana 13 (1997), 411-469. doi: 10.4171/RMI/227