On linear topological properties of 𝐻¹ on spaces of homogeneous type

Müller, Paul F. X.

doi:10.1090/S0002-9947-1990-0974522-7

On linear topological properties of $H^ 1$ on spaces of homogeneous type
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Trans. Amer. Math. Soc. 317 (1990), 463-484 Request permission

Abstract:

Let $(X,d,\mu )$ be a space of homogeneous type. Let $B = \{ x \in X:\mu \{ x\} = 0\}$, then $\mu (B) > 0$ implies that ${H^1}(X,d,\mu )$ contains a complemented copy of ${H^1}(\delta )$. This applies to Hardy spaces ${H^1}(\partial \Omega ,d,\omega )$ associated to weak solutions of uniformly elliptic operators in divergence form. Under smoothness assumptions of the coefficients of the elliptic operators, we obtain that ${H^1}(\partial \Omega ,d,\omega )$ is isomorphic to ${H^1}(\delta )$.

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