Fourier multipliers and their applications to PDE on the quantum Euclidean space

2025/04/10 by Ruzhansky, M., Shaimardan, S., Tulenov, K.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.07604

Abstract

In this work, we present some applications of the L^p-L^q boundedness of Fourier multipliers to PDEs on the noncommutative (or quantum) Euclidean space. More precisely, we establish L^p-L^q norm estimates for solutions of heat, wave, and Schrödinger type equations with Caputo fractional derivative in the case 1 < p ≤ 2 ≤ q < ∞. Moreover, we obtain well-posedness of nonlinear heat and wave equations on the noncommutative Euclidean space.

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