Sobolev Type Embeddings in the Limiting Case.

Michael Cwikel; Evgeniy Pustylnik

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An embedding theorem for Sobolev type functions with gradients in a Lorentz space

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The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.