Abstract
Salem type conditions for trigonometric series are extended to functions from the Wiener algebra. While in the earlier one-dimensional generalization the conditions are given in terms of the Hilbert transform, for the multivariate setting all reasonable singular integrals are equally involved.
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Acknowledgements
In November, 2019, the author took part in the conference “New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative”, at Chapman University in Orange, CA, USA. This work is a natural multidimensional extension of the author’s one-dimensional study presented as a conference talk. It was inspired largely to the stimulating effect of the meeting and numerous discussions with participants. The author greatly appreciates the efforts of the organizers to create such an atmosphere.
The author also thanks the referee for valuable suggestions.
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Liflyand, E. (2021). The Wiener Algebra and Singular Integrals. In: Alpay, D., Peretz, R., Shoikhet, D., Vajiac, M.B. (eds) New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative. Operator Theory: Advances and Applications(), vol 286. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-76473-9_10
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DOI: https://doi.org/10.1007/978-3-030-76473-9_10
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