Fourier multiplier on noncommutative torus and its applications to nonlinear equations
Shaimardan S. Tastankul R.A. Tulenov K.S.
January 2026Springer Science and Business Media Deutschland GmbH
Mathematische Zeitschrift
2026#312Issue 1
In this paper, we present a short and a simple proof of Lp–Lq boundedness of Fourier multipliers on noncommutative torus. We also obtain the Paley type inequality with the same approach. As applications of these results, we establish norm estimates for the solutions of heat and wave type equations which is given by the Caputo fractional derivative on the noncommutative torus. Finally, we obtain local well-posedness in time of nonlinear heat and wave equations in this noncommutative setting.
Fourier multiplier , Hausdorff–Young inequality , Noncommutative torus
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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematics and Statistics, University of New South Wales, Kensington, 2052, NSW, Australia
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
School of Mathematics and Statistics
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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026