arXiv subjects

S. Shaimardan

Publications and source records attributed to S. Shaimardan.

2 recordsLinked to original sources

arXiv2025

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

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 Schr\"odinger type equations with Caputo fractional derivative in the case $1 < p \leq 2 \leq q < \infty.$ Moreover, we obtain well-posedness of nonlinear heat and wave equations on the noncommutative Euclidean space.

math.AP↗

arXiv2023

$L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces

In this paper, we study Fourier multipliers on quantum Euclidean spaces and obtain results on their $L^p -L^q$ boundedness. On the way to get these results, we prove Paley, Hausdorff-Young-Paley, and Hardy-Littlewood inequalities on the quantum Euclidean space. As applications, we establish the $L^p -L^q$ estimate for the heat semigroup and Sobolev embedding theorem on quantum Euclidean spaces. We also obtain quantum analogues of the logarithmic Sobolev and Nash type inequalities.

math.FA↗