An extended version of the Maz’ya–Shaposhnikova theorem on the limit as s→ 0 + of the Gagliardo–Slobodeckij fractional seminorm is established in the Orlicz space setting. Our result holds in fractional Orlicz–Sobolev spaces associated with Young functions satisfying the Δ_2-condition, and, as shown by counterexamples, it may fail if this condition is dropped.
On the Limit as s→ 0 + of Fractional Orlicz–Sobolev Spaces / Alberico A.; Cianchi A.; Pick L.; Slavikova L.. - In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. - ISSN 1069-5869. - STAMPA. - 26:(2020), pp. 0-0. [10.1007/s00041-020-09785-z]
On the Limit as s→ 0 + of Fractional Orlicz–Sobolev Spaces
Cianchi A.
;
2020
Abstract
An extended version of the Maz’ya–Shaposhnikova theorem on the limit as s→ 0 + of the Gagliardo–Slobodeckij fractional seminorm is established in the Orlicz space setting. Our result holds in fractional Orlicz–Sobolev spaces associated with Young functions satisfying the Δ_2-condition, and, as shown by counterexamples, it may fail if this condition is dropped.
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