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.
Fractional Orlicz-Sobolev embeddings / Alberico A.; Cianchi A.; Pick L.; Slavikova L.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 149:(2021), pp. 216-253. [10.1016/j.matpur.2020.12.007]
Fractional Orlicz-Sobolev embeddings
Cianchi A.
;
2021
Abstract
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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