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<p>In this paper, we present a short and a simple proof of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>–<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^{q}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>q</mi> </msup> </math></EquationSource> </InlineEquation> 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.</p>

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Fourier multiplier on noncommutative torus and its applications to nonlinear equations

  • 期刊论文

  • 发表日期：

    2025年11月10日

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  • S. Shaimardan,
  • R. A. Tastankul,
  • K. S. Tulenov

摘要

In this paper, we present a short and a simple proof of \(L^{p}\) L p – \(L^{q}\) L q 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.