DOI QR코드

DOI QR Code

FINITE DIMENSIONAL SUBSPACES OF A BESOV SPACE

  • Hee Chul Pak (Department of Mathematics Dankook University)
  • Received : 2023.04.15
  • Accepted : 2023.05.16
  • Published : 2023.05.30

Abstract

It is concerned with the size of bounded functions in Besov spaces. It reports that every closed subspace consisted with bounded functions in Besov spaces Bsp,p(𝕋d) (s < 0) is finite dimensional.

Keywords

Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2021R1I1A305247113).

References

  1. O. V. Besov, On a family of function spaces. Embedding theorems and applications (in Russian), Dokl. Akad. Nauk SSSR, 126 (1959), 1163-1165.
  2. O. V. Besov, On a family of function spaces in connection with embeddings and extensions (in Russian), Trudy Mat. Inst. Steklov, 60 (1961), 42-81.
  3. H. Han, H. Pak, Resolvent inequality of Laplacian in Besov spaces, J. Chungcheong Math. Soc., 22 (2009), 117-121.
  4. L. Hormander, Linear Partial Differential Operators, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1963.
  5. J. Peetre, Sur les espaces de Besov, C. R. Acad. Sci. Paris, 264 (1967), 281-283.
  6. H. Triebel, Theory of function spaces II, Birkhauser, 1992.