Definitions of Sobolev Classes on Metric Spaces
نویسنده
چکیده
There are several ways to generalize the notion of the Sobolev space to the setting of metric spaces equipped with a Borel measure. We describe next two definitions of the Sobolev space on a metric space (S, d) equipped with a Borel masure μ that is finite on every ball. Following [11], for 1 ≤ p < ∞, we define the Sobolev space M(S, d, μ) as the set of all u ∈ L(S) for which there exists 0 ≤ g ∈ L(S) such that the inequality
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