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• # Artykuł - szczegóły

## Colloquium Mathematicum

2010 | 118 | 1 | 13-41

## H¹ and BMO for certain locally doubling metric measure spaces of finite measure

EN

### Abstrakty

EN
In a previous paper the authors developed an H¹-BMO theory for unbounded metric measure spaces (M,ρ,μ) of infinite measure that are locally doubling and satisfy two geometric properties, called "approximate midpoint" property and "isoperimetric" property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies to a class of unbounded, complete Riemannian manifolds of finite measure and to a class of metric measure spaces of the form $(ℝ^{d},ρ_{φ}, μ_{φ})$, where $dμ_{φ} = e^{-φ} dx$ and $ρ_{φ}$ is the Riemannian metric corresponding to the length element $ds² = (1+|∇φ|)² (dx₁² + ⋯ + dx²_{d})$. This generalizes previous work of the last two authors for the Gauss space.

13-41

wydano
2010

### Twórcy

autor
• Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy
autor
• Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy
autor
• Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via R. Cozzi 53, 20125 Milano, Italy