The dual of Besov spaces on fractals

• Autorzy: Alf Jonsson , Hans Wallin
• Języki publikacji: EN

Abstrakty

EN

For certain classes of fractal subsets F of $ℝ^n$, the Besov spaces $B_α^{p,q}(F)$ have been studied for α > 0 and 1 ≤ p,q ≤ ∞. In this paper the Besov spaces $B_α^{p,q}(F)$ are introduced for α < 0, and it is shown that the dual of $B_α^{p,q}(F)$ is $B_{-α}^{p',q'}(F), α ≠ 0, 1 < p,q < ∞, where 1/p + 1/p' = 1, 1/q + 1/q' = 1.

Kategorie tematyczne

• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994-1995
• Tom: 112
• Numer: 3
• Strony: 285-300

Daty

wydano

1995

otrzymano

1993-12-31

poprawiono

1994-04-26

Twórcy

autor

Alf Jonsson

• Department of Mathematics, University of Umeå, S-901 87 Umeå, Sweden

autor

Hans Wallin

• Department of Mathematics, University of Umeå, S-901 87 Umeå, Sweden

Bibliografia

• [1] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799.
• [2] A. Jonsson, Markov's inequality and local polynomial approximation, in: Lecture Notes in Math. 1302, Springer, Berlin, 1986, 303-316.
• [3] A. Jonsson, The duals of Lipschitz spaces defined on closed sets, Indiana Univ. Math. J. 39 (1990), 467-476.
• [4] A. Jonsson, Besov spaces on closed sets by means of atomic decompositions, Department of Math., University of Umeå, preprint No. 7, 1993.
• [5] A. Jonsson and H. Wallin, Function Spaces on Subsets of $ℝ^n$, Math. Reports 2, Part 1, Harwood Acad. Publ., 1984.
• [6] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983.
• [7] H. Wallin, Self-similarity, Markov's inequality and d-sets, in: Proc. Conf. Varna, 1991, to appear.