A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin-Triebel spaces with mixed norms
By Jon Johnsen, Winfried Sickel. 2017
61 citations recorded by the source corpus.
The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin–Triebel spaces (that contain the Lp-Sobolev spaces Hps as special cases). The method extends to a proof of the corresponding fact for general Lizorkin–Triebel spaces based on mixed Lp-norms. In this context a Nikol' skij–Plancherel–Polya inequality for sequences of functions satisfying a geometric rectangle condition is proved. The results extend also to anisotropic spaces of the quasi-homogeneous type.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/d915038b1df19f5306ae049257637c6862c9b153
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In Applied Mathematics
- Dachun Yang
- Wen Yuan
- Long Huang
- Jun Liu
- Athanasios G. Georgiadis
- Morten Nielsen
- Jon Johnsen
- Jan Vyb'iral
Citations in the corpus
- Anisotropic function spaces and maximal regularity for parabolic problems Part 1: Function spaces (2009, unknown): “Sickel [41].”
- SOBOLEV AND JAWERTH EMBEDDINGS FOR SPACES WITH VARIABLE SMOOTHNESS AND INTEGRABILITY (2009, methodology): “[22] Johnsen, J., and W. Sickel: A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms.”
- On Function Spaces with Mixed Norms — A Survey (2019, background): “For more progresses about various function spaces with mixed norms and their applications in the boundedness of different operators, we refer the reader to [18, 20, 22, 33, 34, 38, 39, 47–50].”
- Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, background): “For more developments of mixed-norm function spaces, we refer the reader to [16, 18, 27, 29, 42, 43].”
- Wavelet transforms for homogeneous mixed-norm Triebel–Lizorkin spaces (2016, methodology): “For contributions on the embedding properties and traces on hyperplanes, the reader is referred to works of Johnsen and Sickel [23, 24], who in collaboration with Munch Hansen also analysed embeddings and equivalent characterisations of such mixed-norm spaces, their invariance under coordinate trans”