In this note we prove the validity of the Maz'ya-Shaposhnikova formula in magnetic fractional Orlicz-Sobolev spaces. This complements a previous asymptotic study of the limit as s ↑ 1 performed by the second author in ...

We obtain improved fractional Poincaré and Sobolev-Poincaré inequalities including powers of the distance to the boundary in bounded John, s-John, and Hölder-α domains, and discuss their optimality.

In this article, we define a class of fractional Orlicz–Sobolev spaces on Carnot groups, and in the spirit of the celebrated results of Bourgain–Brezis–Mironescu and of Maz’ya–Shaposhnikova, we study the asymptotic behaviour ...

We consider a homogeneous fractional Sobolev space obtained by completion of the space of smooth test functions, with respect to a Sobolev–Slobodeckiĭ norm. We compare it to the fractional Sobolev space obtained by the ...

In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p: Ω × Ω → (1,∞) and q : ∂Ω → (1,∞) are continuous functions such that (n − 1)p(x, x) n − sp(x, x) > ...

In this paper, we obtain improved versions of Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities, involving Besov norms of negative smoothness. As an application of the former, we derive the existence of extremals of ...