Abstract:
We study the properties of the so-called grand Sobolev spaces on a metric measure space. The introduction of the spaces is motivated by the available pointwise description of the elements of the spaces in the Euclidean case. We obtain a continuous embedding of the grand Sobolev space into a space of integrable functions under some regularity condition on the metric measure space.
Keywords:grand Lebesgue spaces, grand Sobolev spaces, regular metric measure spaces.
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