Variants of the maximal double Hilbert transform

Prestini, Elena

doi:10.1090/S0002-9947-1985-0792826-6

Variants of the maximal double Hilbert transform
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by Elena Prestini

Trans. Amer. Math. Soc. 290 (1985), 761-771

DOI: https://doi.org/10.1090/S0002-9947-1985-0792826-6

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Abstract:

We prove the boundedness on ${L_p}({T^2})$, $1 < p < \infty$, of two variants of the double Hilbert transform and maximal double Hilbert transform. They have an application to a problem of almost everywhere convergence of double Fourier series.

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