# ${H}^{1}$-BMO duality on graphs

Colloquium Mathematicae (2000)

- Volume: 86, Issue: 1, page 67-91
- ISSN: 0010-1354

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topRuss, Emmanuel. "$H^1$-BMO duality on graphs." Colloquium Mathematicae 86.1 (2000): 67-91. <http://eudml.org/doc/210842>.

@article{Russ2000,

abstract = {On graphs satisfying the doubling property and the Poincaré inequality, we prove that the space $H^\{1\}_\{max\}$ is equal to $H_\{at\}^\{1\}$, and therefore that its dual is BMO. We also prove the atomic decomposition for $H^\{p\}_\{max\}$ for p ≤ 1 close enough to 1.},

author = {Russ, Emmanuel},

journal = {Colloquium Mathematicae},

keywords = {Markov kernel; atomic decomposition; -BMO; maximal Hardy space; BMO space; infinite connected graph; Riemannian manifold; doubling property},

language = {eng},

number = {1},

pages = {67-91},

title = {$H^1$-BMO duality on graphs},

url = {http://eudml.org/doc/210842},

volume = {86},

year = {2000},

}

TY - JOUR

AU - Russ, Emmanuel

TI - $H^1$-BMO duality on graphs

JO - Colloquium Mathematicae

PY - 2000

VL - 86

IS - 1

SP - 67

EP - 91

AB - On graphs satisfying the doubling property and the Poincaré inequality, we prove that the space $H^{1}_{max}$ is equal to $H_{at}^{1}$, and therefore that its dual is BMO. We also prove the atomic decomposition for $H^{p}_{max}$ for p ≤ 1 close enough to 1.

LA - eng

KW - Markov kernel; atomic decomposition; -BMO; maximal Hardy space; BMO space; infinite connected graph; Riemannian manifold; doubling property

UR - http://eudml.org/doc/210842

ER -

## References

top- [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. Zbl0933.60047
- [CAR] L. Carleson, Two remarks on ${H}^{1}$ and BMO, Adv. Math. 22 (1976), 269-277. Zbl0357.46058
- [COI] R. Coifman, A real-variable characterization of ${H}^{p}$, Studia Math. 51 (1974), 269-274. Zbl0289.46037
- [CW] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. Zbl0358.30023
- [DEL1] T. Delmotte, Versions discrètes de l'inégalité de Harnack, thesis, University of Cergy-Pontoise, 1997.
- [DEL2] T. Delmotte, Parabolic Harnack inequality and estimates of Markov chains on graphs, Rev. Mat. Iberoamericana 15 (1999), 181-232. Zbl0922.60060
- [HOR] L. Hörmander, ${L}^{p}$ estimates for (pluri-)subharmonic functions, Math. Scand. 20 (1967), 65-78. Zbl0156.12201
- [LAT] R. H. Latter, A decomposition of ${H}^{p}\left({\mathbb{R}}^{n}\right)$ in terms of atoms, Studia Math. 62 (1978), 92-101.
- [MS1] R. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. Math. 33 (1979), 257-270. Zbl0431.46018
- [MS2] R. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, Adv. Math. 33 (1979), 271-309. Zbl0431.46019
- [MEY] Y. Meyer, Dualité entre ${H}^{1}$ et BMO sur les espaces de type homogène par Lennart Carleson, unpublished notes.
- [RUS] E. Russ, ${H}^{1}$-BMO duality on Riemannian manifolds, preprint.
- [SC] L. Saloff-Coste, Analyse sur les groupes de Lie à croissance polynomiale, Ark. Mat. 28 (1990), 315-331. Zbl0715.43009
- [ST] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993.
- [UCH] A. Uchiyama, A maximal function characterization of ${H}^{p}$ on the space of homogeneous type, Trans. Amer. Math. Soc. 262 (1980), 579-592. Zbl0503.46020

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