Titlebook: Extended Abstracts 2021/2022; Ghent Analysis and P Michael Ruzhansky,Karel Van Bockstal Book 2024 The Editor(s) (if applicable) and The Aut

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Acumen

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Log-Sobolev and Nash Inequalities on Graded Groupsjoint work Chatzakou et al. (Logarithmic Sobolev inequalities on Lie groups (2021). arXiv:2106.15652) with A. Kassymov and M. Ruzhansky. These inequalities include the logarithmic Sobolev inequality on graded groups, its semi-probabilistic equivalent on stratified groups, referred to as the “semi-Ga

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Boundedness of Fourier Multipliers on Fundamental Domains of Latticesutline of Fourier analysis on fundamental domains, then use interpolation techniques to obtain some inequalities and conclude with a Hörmander-type boundedness theorem. At the end, I present some current research perspectives.

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Pointwise Domination and Weak , Boundedness of Littlewood-Paley Operators via Sparse Operatorslts of Shi et al. (J. Math. Pures Appl. 101:394–413, 2014) significantly. In particular, the new proof for Shi et al. (J. Math. Pures Appl. 101:394–413, 2014; Theorem 1.1) is quite short and, unlike the original proof, does not rely on the properties of the “Marcinkiewicz function”. This allows us t

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