Anisotropic Lizorkin–Triebel spaces with mixed norms — traces on smooth boundaries

By Jon Johnsen, S. Hansen, Winfried Sickel. 2015

54 citations recorded by the source corpus.

This article deals with trace operators on anisotropic Lizorkin–Triebel spaces with mixed norms over cylindrical domains with smooth boundary. As a preparation we include a rather self‐contained exposition of Lizorkin–Triebel spaces on manifolds and extend these results to mixed‐norm Lizorkin–Triebel spaces on cylinders in Euclidean space. In addition Rychkov's universal extension operator for a half space is shown to be bounded with respect to the mixed norms, and a support preserving right‐inverse of the trace is given explicitly and proved to be continuous in the scale of mixed‐norm Lizorkin–Triebel spaces. As an application, the heat equation is considered in these spaces, and the necessary compatibility conditions on the data are deduced.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/74b0ec5e339464322282e164ec4160408601c7f5

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In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Long Huang
4. Jun Liu
5. Yangyang Zhang
6. Yoshihiro Sawano
7. Songbai Wang
8. Ciqiang Zhuo

Citations in the corpus

• Dual spaces of anisotropic mixed-norm Hardy spaces (2018, background): “In addition, the theory of anisotropic or mixed-norm function spaces was developed well in recent years; see, for example, [6, 7, 9, 14, 18].”
• Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, background): “For more progresses about this theory, we refer the reader to [5, 19, 23, 24, 39, 40, 41, 76, 77].”