On graphs satisfying the doubling property and the Poincaré inequality, we prove that the space is equal to , and therefore that its dual is BMO. We also prove the atomic decomposition for for p ≤ 1 close enough to 1.
@article{bwmeta1.element.bwnjournal-article-cmv86i1p67bwm, author = {Emmanuel Russ}, title = {$H^1$-BMO duality on graphs}, journal = {Colloquium Mathematicae}, volume = {84/85}, year = {2000}, pages = {67-91}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p67bwm} }
Russ, Emmanuel. $H^1$-BMO duality on graphs. Colloquium Mathematicae, Tome 84/85 (2000) pp. 67-91. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p67bwm/
[000] [AC] P. Auscher and T. Coulhon, Gaussian lower bounds for random walks from elliptic regularity, Ann. Inst. H. Poincaré Probab. Statist. 35 (1999), 605-630. | Zbl 0933.60047
[001] [CAR] L. Carleson, Two remarks on and BMO, Adv. Math. 22 (1976), 269-277. | Zbl 0357.46058
[002] [COI] R. Coifman, A real-variable characterization of , Studia Math. 51 (1974), 269-274. | Zbl 0289.46037
[003] [CW] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. | Zbl 0358.30023
[004] [DEL1] T. Delmotte, Versions discrètes de l'inégalité de Harnack, thesis, University of Cergy-Pontoise, 1997.
[005] [DEL2] T. Delmotte, Parabolic Harnack inequality and estimates of Markov chains on graphs, Rev. Mat. Iberoamericana 15 (1999), 181-232. | Zbl 0922.60060
[006] [HOR] L. Hörmander, estimates for (pluri-)subharmonic functions, Math. Scand. 20 (1967), 65-78. | Zbl 0156.12201
[007] [LAT] R. H. Latter, A decomposition of in terms of atoms, Studia Math. 62 (1978), 92-101.
[008] [MS1] R. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. Math. 33 (1979), 257-270. | Zbl 0431.46018
[009] [MS2] R. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, Adv. Math. 33 (1979), 271-309. | Zbl 0431.46019
[010] [MEY] Y. Meyer, Dualité entre et BMO sur les espaces de type homogène par Lennart Carleson, unpublished notes.
[011] [RUS] E. Russ, -BMO duality on Riemannian manifolds, preprint.
[012] [SC] L. Saloff-Coste, Analyse sur les groupes de Lie à croissance polynomiale, Ark. Mat. 28 (1990), 315-331. | Zbl 0715.43009
[013] [ST] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993.
[014] [UCH] A. Uchiyama, A maximal function characterization of on the space of homogeneous type, Trans. Amer. Math. Soc. 262 (1980), 579-592. | Zbl 0503.46020