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Singular Integrals on Product Spaces Related to the Carleson Operator

Published online by Cambridge University Press:  20 November 2018

Elena Prestini
Elena Prestini*
Affiliation:
Departimento di Matematica, Seconda Università di Roma, 00133 Rome, Italy e-mail: prestini@mat.uniroma2.it
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Abstract

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We prove ${{L}^{p}}({{\mathbb{T}}^{2}})$ boundedness, $1\,<\,p\,\le \,2$, of variable coefficients singular integrals that generalize the double Hilbert transform and present two phases that may be of very rough nature. These operators are involved in problems of a.e. convergence of double Fourier series, likely in the role played by the Hilbert transform in the proofs of a.e. convergence of one dimensional Fourier series. The proof due to C.Fefferman provides a basis for our method.

Keywords

42B2042B08
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 1 , 01 February 2006 , pp. 154 - 179
Copyright
Copyright © Canadian Mathematical Society 2006

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