Symmetries on manifolds: generalizations of the radial lemma of Strauss

Grosse N, Schneider C (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Revista Matematica Complutense Springer Verlag (Germany)

Book Volume: 32

Pages Range: 365-393

Journal Issue: 2

DOI: 10.1007/s13163-018-0285-2

Abstract

For a compact subgroup G of the group of isometries acting on a Riemannian manifold M we investigate subspaces of Besov and Triebel–Lizorkin type which are invariant with respect to the group action. Our main aim is to extend the classical Strauss lemma under suitable assumptions on the Riemannian manifold by proving that G-invariance of functions implies certain decay properties and better local smoothness. As an application we obtain inequalities of Caffarelli–Kohn–Nirenberg type for G-invariant functions. Our results generalize those obtained in Skrzypczak (Rev Mat Iberoam 18:267–299, 2002). The main tool in our investigations are atomic decompositions adapted to the G-action in combination with trace theorems.

Authors with CRIS profile

Cornelia Schneider Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

Involved external institutions

Albert-Ludwigs-Universität Freiburg DE Germany (DE)

How to cite

APA:

Grosse, N., & Schneider, C. (2019). Symmetries on manifolds: generalizations of the radial lemma of Strauss. Revista Matematica Complutense, 32(2), 365-393. https://dx.doi.org/10.1007/s13163-018-0285-2

MLA:

Grosse, Nadine, and Cornelia Schneider. "Symmetries on manifolds: generalizations of the radial lemma of Strauss." Revista Matematica Complutense 32.2 (2019): 365-393.

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