Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Multiplicatively invariant subspaces of Besov spaces


Author: Per Nilsson
Journal: Trans. Amer. Math. Soc. 265 (1981), 535-543
MSC: Primary 46E35
DOI: https://doi.org/10.1090/S0002-9947-1981-0610964-1
MathSciNet review: 610964
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study subspaces of Besov spaces $ B_p^{s,q}$ which are invariant under pointwise multiplication by characters. The case $ s > 0$ is completely described, and for the case $ s \leqslant 0$ we extend known results.


References [Enhancements On Off] (What's this?)

  • [1] J. Bergh and J. Löfström, Interpolation spaces. An introduction, Springer, Berlin and New York, 1976. MR 0482275 (58:2349)
  • [2] S. Campanato, Proprietà di una famiglia di spazi funzionali, Ann. Scuola Norm. Sup. Pisa 18 (1964), 137-160. MR 0167862 (29:5127)
  • [3] E. Gagliardo, A unified structure in various families of function spaces. Compactness and closure theorems, Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960), Jerusalem Academic Press, Jerusalem; Pergamon, Oxford, 1961. MR 0133000 (24:A2836)
  • [4] R. Johnson, Maximal subspaces of Besov spaces invariant under multiplication by characters, Trans. Amer. Math. Soc. 249 (1979), 387-407. MR 525680 (80h:46042)
  • [5] -, Duality methods for the study of maximal subspaces of Besov spaces invariant under multiplication by characters, Univ. of Maryland Tech. Report 79, 75.
  • [6] C. B. Morrey, Functions of several variables and absolute continuity, Duke Math. J. 6 (1940), 187-215. MR 0001279 (1:209a)
  • [7] J. Peetre, On the theory of $ {L_{p,\lambda }}$ spaces, J. Funct. Anal. 4 (1969), 71-87. MR 0241965 (39:3300)
  • [8] -, New thoughts on Besov spaces, Duke Univ. Math. Ser. Durham, N. C., 1976. MR 0461123 (57:1108)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E35

Retrieve articles in all journals with MSC: 46E35


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0610964-1
Keywords: Besov spaces, Morrey spaces, pointwise multipliers
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society