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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https://doi.org/10.1007/978-981-10-6150-9hed. Actually, we obtain weighted critical Sobolev-type identities. Furthermore, anisotropic versions of these identities with any homogeneous quasi-norm are presented. Finally, we discuss hypoelliptic versions of these results in the setting of stratified Lie groups.

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Pointwise Domination and Weak , Boundedness of Littlewood-Paley Operators via Sparse Operators3, 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 to get a precise linear dependence on Dini constants with a subsequent application to Littlewood–Paley operators by the well-known techniques.

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Boundedness of Fourier Multipliers on Graded Lie Groupsoperators on an arbitrary graded Lie group ., where . is the Hardy spaces on .. Our main result extends those obtained by Fischer and Ruzhansky (Colloq Math 165:1–30, 2021), who proved the . and ., ., boundedness of such Fourier multiplier operators.

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-, Norms of Spectral Multipliersevant .-. norm estimates to spectral multipliers of left-invariant weighted subcoercive operators on unimodular Lie groups. In particular, this includes spectral multipliers of Laplacians, sub-Laplacians and Rockland operators. As an application, we obtain, e.g., time asymptotics for the .-. norms of the heat kernels and Sobolev-type embeddings.

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978-3-031-42541-7The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Extended Abstracts 2021/2022978-3-031-42539-4Series ISSN 2297-0215 Series E-ISSN 2297-024X