The embedding theorem for the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type
HTML articles powered by AMS MathViewer
- by Y.-S. Han
- Proc. Amer. Math. Soc. 123 (1995), 2181-2189
- DOI: https://doi.org/10.1090/S0002-9939-1995-1249880-9
- PDF | Request permission
Abstract:
In this note the classical embedding theorem for the Besov and Triebel-Lizorkin spaces on ${R^n}$ is generalized to the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type. The proof is new even for ${R^n}$ case.References
- Ronald R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin-New York, 1971 (French). Étude de certaines intégrales singulières. MR 0499948, DOI 10.1007/BFb0058946 M. Christ, Singular integral operators, NSF-CBMS Regional Conf. at Missoula, MT, August 1989.
- G. David, J.-L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), no. 4, 1–56 (French). MR 850408, DOI 10.4171/RMI/17
- Y. S. Han and E. T. Sawyer, Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces, Mem. Amer. Math. Soc. 110 (1994), no. 530, vi+126. MR 1214968, DOI 10.1090/memo/0530
- Yves Meyer, Le lemme de Cotlar et Stein et la continuité $L^2$ des opérateurs définis par des intégrales singulières, Astérisque 131 (1985), 115–125 (French). Colloquium in honor of Laurent Schwartz, Vol. 1 (Palaiseau, 1983). MR 816742
- Roberto A. Macías and Carlos Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), no. 3, 257–270. MR 546295, DOI 10.1016/0001-8708(79)90012-4
- Jaak Peetre, New thoughts on Besov spaces, Duke University Mathematics Series, No. 1, Duke University, Mathematics Department, Durham, N.C., 1976. MR 0461123
- Hans Triebel, Theory of function spaces, Monographs in Mathematics, vol. 78, Birkhäuser Verlag, Basel, 1983. MR 781540, DOI 10.1007/978-3-0346-0416-1
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2181-2189
- MSC: Primary 46E35; Secondary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-1995-1249880-9
- MathSciNet review: 1249880