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$H^1$-BMO duality on graphs

100%

Russ E.

Colloquium Mathematicum

2000

tom 86

nr 1

67-91

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.

Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds

63%

Russ E., Sire Y.

Studia Mathematica

2011

tom 203

nr 2

105-127

Let G be a real connected Lie group with polynomial volume growth endowed with its Haar measuredx. Given a C² positive bounded integrable function M on G, we give a sufficient condition for an L² Poincaré inequality with respect to the measure M(x)dx to hold on G. We then establish a nonlocal Poincaré inequality on G with respect to M(x)dx. We also give analogous Poincaré inequalities on Riemannian manifolds and deal with the case of Hardy inequalities.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Russ E.

1 Sire Y.

1 2011

1 2000

Wyniki wyszukiwania

$H^1$-BMO duality on graphs

Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds