Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-10

AUTHORS

Alessio Martini, Alessandro Ottazzi, Maria Vallarino

ABSTRACT

Let G = N ⋊ A, where N is a stratified group and A = ℝ acts on N via automorphic dilations. Homogeneous sub-Laplacians on N and A can be lifted to left-invariant operators on G, and their sum is a sub-Laplacian Δ on G. We prove a theorem of Mihlin–Hörmander type for spectral multipliers of Δ. The proof of the theorem hinges on a Calderón–Zygmund theory adapted to a sub-Riemannian structure of G and on L1-estimates of the gradient of the heat kernel associated to the sub-Laplacian Δ. More... »

PAGES

357-397

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11854-018-0063-6

DOI

http://dx.doi.org/10.1007/s11854-018-0063-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1110711348


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47 schema:description Let G = N ⋊ A, where N is a stratified group and A = ℝ acts on N via automorphic dilations. Homogeneous sub-Laplacians on N and A can be lifted to left-invariant operators on G, and their sum is a sub-Laplacian Δ on G. We prove a theorem of Mihlin–Hörmander type for spectral multipliers of Δ. The proof of the theorem hinges on a Calderón–Zygmund theory adapted to a sub-Riemannian structure of G and on L1-estimates of the gradient of the heat kernel associated to the sub-Laplacian Δ.
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