Lp–Lq boundedness of Fourier multipliers on quantum Euclidean spaces
Ruzhansky M. Shaimardan S. Tulenov K.
January 2026Springer-Verlag Italia s.r.l.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
2026#120Issue 1
In this paper, we study Fourier multipliers on quantum Euclidean spaces and obtain results on their Lp–Lq 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 Lp–Lq estimate for the heat semigroup and Sobolev embedding theorem on quantum Euclidean spaces. We also obtain quantum analogues of logarithmic Sobolev and Nash type inequalities.
Fourier multipliers , Hausdorff–Young inequality , Heat semigroup , Noncommutative Euclidean space , Sobolev embedding
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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
Institute of Mathematics and Mathematical Modeling
School of Mathematical Sciences
Department of Mathematics: Analysis
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