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The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz–Sobolev spaces in Rn. An improved embedding with an Orlicz–Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order s∈(0,1), and higher-order spaces are considered. Related Hardy type inequalities are proposed as well.
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Alberico et al. (2021) studied this question.
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