Embedding Theorem for Inhomogeneous Besov and Triebel–Lizorkin Spaces on RD-spaces
Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 757-773

Voir la notice de l'article provenant de la source Cambridge University Press

In this article we prove an embedding theorem for inhomogeneous Besov and Triebel–Lizorkin spaces on $\text{RD}$ -spaces. The crucial idea is to use the geometric density condition on the measure.
DOI : 10.4153/CMB-2015-028-1
Mots-clés : 42B25, 46F05, 46E35, spaces of homogeneous type, test function space, distributions, Calderón reproducing formula, Besov and Triebel-Lizorkin spaces, embedding
Han, Yanchang. Embedding Theorem for Inhomogeneous Besov and Triebel–Lizorkin Spaces on RD-spaces. Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 757-773. doi: 10.4153/CMB-2015-028-1
@article{10_4153_CMB_2015_028_1,
     author = {Han, Yanchang},
     title = {Embedding {Theorem} for {Inhomogeneous} {Besov} and {Triebel{\textendash}Lizorkin} {Spaces} on {RD-spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {757--773},
     year = {2015},
     volume = {58},
     number = {4},
     doi = {10.4153/CMB-2015-028-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-028-1/}
}
TY  - JOUR
AU  - Han, Yanchang
TI  - Embedding Theorem for Inhomogeneous Besov and Triebel–Lizorkin Spaces on RD-spaces
JO  - Canadian mathematical bulletin
PY  - 2015
SP  - 757
EP  - 773
VL  - 58
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-028-1/
DO  - 10.4153/CMB-2015-028-1
ID  - 10_4153_CMB_2015_028_1
ER  - 
%0 Journal Article
%A Han, Yanchang
%T Embedding Theorem for Inhomogeneous Besov and Triebel–Lizorkin Spaces on RD-spaces
%J Canadian mathematical bulletin
%D 2015
%P 757-773
%V 58
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-028-1/
%R 10.4153/CMB-2015-028-1
%F 10_4153_CMB_2015_028_1

[Chr] [Chr] Christ, M., A T(b) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61 (1990), no. 2, 601–628. Google Scholar

[CW1] [CW1] Coifman, R.R. and Weiss, G., Analyse harmonique non-commutative sur certains espaces homogènes. Étude de certaines intégrales singulières, Lecture Notes in Math. 242, Springer-Verlag, Berlin, 1971. Google Scholar

[CW2] [CW2] Coifman, R.R. and Weiss, G., Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569–645. http://dx.doi.Org/10.1090/S0002-9904-1977-14325-5 Google Scholar

[DJDS] [DJDS] David, G., Journé, J.-L. and Semmes, S., Calderôn-Zygmund operators, para-accretive functions and interpolation, Rev. Mat. Iberoamericana 1 (1985), no. 4,1-56. http://dx.doi.Org/10.4171/RM1/17 Google Scholar

[DH] [DH] Deng, D. and Han, Y.S., Harmonic analysis on spaces of homogeneous type, Lecture Notes in Math., vol. 1966, Springer-Verlag, Berlin, 2009, with a preface by Yves Meyer. Google Scholar

[FS] [FS] Fefferman, C. and Stein, E.M., HP spaces of several variables, Acta Math. 129 (1972), 137–195. http://dx.doi.Org/10.1007/BF02392215 Google Scholar

[FJ] [FJ] Frazier, M. and Jawerth, B., A discrete transform and decomposition of distribution spaces, J. Funct. Anal. 93 (1990), 34–170. http://dx.doi.Org/10.1016/0022-1236(90)90137-A Google Scholar

[HI] [HI] Han, Y.S., Calderon-type reproducing formula and the Tb theorem, Rev. Mat. Iberoamericana 10 (1994), 51–91. Google Scholar

[H2] [H2] Han, Y.S., Plancherel-Pôlya type inequality on spaces of homogeneous type and its applications, Proc. Amer. Math. Soc. 126 (1998), no. 11, 3315–3327. http://dx.doi.Org/10.1090/S0002-9939-98-04445-1 Google Scholar

[H3] [H3] Han, Y.S., Embedding theorem for the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type, Proc. Amer. Math. Soc. 123 (1995), 2181–2189. http://dx.doi.Org/10.1090/S0002-9939-1995-1249880-9 Google Scholar

[HL] [HL] Han, Y.S. and Lin, C., Embedding theorem on spaces of homogeneous type, J. Fourier Anal. Appl. 8(2002), 291–307. http://dx.doi.Org/10.1007/s00041-002-004-5 Google Scholar

[HS] [HS] Han, Y.S. 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 pp. Google Scholar

[HMY1] [HMY1] Han, Y.S., Millier, D. and Yang, D., A theory of Besov and Triebel-Lizorkin spaces on metric measure spaces modeled on Carnot-Carathéodory spaces, Abstr. Appl. Anal., Vol. 2008, Article ID 893409. 250 pages. Google Scholar

[HMY2] [HMY2] Han, Y.S., Millier, D. and Yang, D., Littlewood-Paley characterizations for Hardy spaces on spaces of homogeneous type, Mathematische Nachrichten 279(2006), 1505–1537. http://dx.doi.Org/10.1 OO2/mana.2OO610435 Google Scholar

[J] [J] Jawerth, B., Some observations on Besov and Lizorkin-Triebel spaces, Math. Scand. 40 (1977), 94–104. Google Scholar

[MS] [MS] Macias, R.A. and Segovia, C., Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257–270. http://dx.doi.Org/10.1016/0001-8708(79)90012-4 Google Scholar

[NS] [NS] Nagel, A. and Stein, E.M., On the product theory of singular integrals, Rev. Mat. Iberoamericana 20 (2004), 531–561. http://dx.doi.Org/10.4171/RMI/400 Google Scholar

[SI] [SI] Sturm, K. T., On the geometry of measure spaces I, Acta Math. 196, (2006), 65–131. http://dx.doi.Org/10.1007/s11511-006-0002-8 Google Scholar

[S2] [S2] Sturm, K. T., On the geometry of measure spaces II, Acta Math. 196, (2006), 133–177. http://dx.doi.Org/10.1007/s11511-006-0003-7 Google Scholar

[T] [T] Triebel, H., Theory of Function Spaces, Birkhâuser-Verlag, Basel, 1983. Google Scholar

[Y] [Y] Yang, D., Embedding theorems ofBesov and Lizorkin-Triebel spaces on spaces of homogeneous type, Science in China, Series A Mathematics 46, (2003), 187–199. http://dx.doi.Org/10.1360/03ys9020 Google Scholar

Cité par Sources :