ON q-DEFORMATED HÖRMANDER MULTIPLIER THEOREM
Tokmagambetov N.S.
30 September 2025al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2025#127Issue 3117 - 135 pp.
The main purposes of this work, we introduce the q-deformed Fourier multiplier Ag defined on the space L2q(Rq) through the framework of the q2-Fourier transform, while also extending the functional setting of Lpq(Rq) with 1 ≤ p < ∞. Our approach provides a natural extension of classical Fourier multiplier theory into the q-deformed setting, which is relevant in the context of quantum groups and noncommutative analysis. Furthermore, we establish several key q-analogues of classical harmonic analysis inequalities for the q2-Fourier transform, including the Paley inequality, Hausdorff-Young inequality, Hausdorff-Young-Paley inequality, and Hardy-Littlewood inequality. These results not only generalize their classical counterparts but also open new avenues for analysis on q-deformed spaces. As a significant application, we prove a q-deformed version of the Hörmander multiplier theorem, which provides sufficient conditions for the boundedness of multipliers in the q-deformed setting. This work sets the stage for further developments in the field of q-deformed harmonic analysis.
Fourier multiplier , Hausdorff-Young inequality , inequality , multiplier , q-caclulus , q-Jackson integral
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Karaganda Buketov University, Karaganda, Kazakhstan
Karaganda Buketov University
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