H 1 -BMO duality on graphs

Emmanuel Russ

Colloquium Mathematicae (2000)

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

Abstract

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On graphs satisfying the doubling property and the Poincaré inequality, we prove that the space H m a x 1 is equal to H a t 1 , and therefore that its dual is BMO. We also prove the atomic decomposition for H m a x p for p ≤ 1 close enough to 1.

How to cite

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Russ, 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

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  10. [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
  11. [MEY] Y. Meyer, Dualité entre H 1 et BMO sur les espaces de type homogène par Lennart Carleson, unpublished notes. 
  12. [RUS] E. Russ, H 1 -BMO duality on Riemannian manifolds, preprint. 
  13. [SC] L. Saloff-Coste, Analyse sur les groupes de Lie à croissance polynomiale, Ark. Mat. 28 (1990), 315-331. Zbl0715.43009
  14. [ST] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993. 
  15. [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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