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Embeddings into Orlicz spaces via the modified Riesz potential

Published 3 Aug 2015 in math.FA and math.CA | (1508.00362v1)

Abstract: We study point-wise estimates for the modified Riesz potential. We show that the point-wise estimates imply embeddings into Orlicz spaces from the L1_p-space where the functions are defined in non-smooth domains. The Orlicz functions depend on the geometry of the domain. We show that the Orlicz function is optimal when p=1.

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