Littlewood–Paley decompositions and Besov spaces on Lie groups of polynomial growth

By G. Furioli, Camillo Melzi, Alessandro Veneruso. 2005

87 citations recorded by the source corpus.

We introduce a Littlewood–Paley decomposition related to any sub‐Laplacian on a Lie group G of polynomial volume growth; this allows us to prove a Littlewood–Paley theorem in this general setting and to provide a dyadic characterization of Besov spaces B s,q p (G ), s ∈ ℝ, equivalent to the classical definition through the heat kernel. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/0ca6ea60c46f9d9e8755034446f1e875817199c6

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In Applied Mathematics

1. Dachun Yang
2. D. Müller
3. S. Tikhonov
4. E. Nursultanov
5. Michael Ruzhansky
6. Yuan Zhou
7. Wen Yuan
8. Pekka Koskela

Citations in the corpus

• Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds (2014, methodology): “In addition, using the Littlewood-Paley decomposition, one can also use the characterisation given in [FMV06].”
• A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces (2009, background): “Since Hajłasz in [13] introduced Sobolev spaces on any metric measure space, a series of papers has been devoted to the construction and investigation of Sobolev spaces of various types on metric measure spaces; see, for example, [15, 30, 8, 10, 31, 42, 20, 21, 28, 5, 14, 9, 49].”