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Transactions of the American Mathematical Society

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On linear topological properties of $ H\sp 1$ on spaces of homogeneous type

Author: Paul F. X. Müller
Journal: Trans. Amer. Math. Soc. 317 (1990), 463-484
MSC: Primary 46E15; Secondary 46B20
MathSciNet review: 974522
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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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