We continue the study of the space BV α(Rn) of functions with bounded fractional variation in
Rn and of the distributional fractional Sobolev space Sα, p (Rn), with p∈[1,+∞] and α∈(0 …

We continue the study of the space BV α (R n) of functions with bounded fractional variation
in R n of order α∈(0, 1) introduced in our previous work (Comi and Stefani in J Funct Anal …

Extended versions of the Bourgain–Brezis–Mironescu theorems on the limit as s! 1Ą of the
Gagliardo–Slobodeckij fractional seminorm are established in the Orlicz space setting. Our …

Under certain restrictions on s, p, q, the Triebel-Lizorkin spaces can be viewed as
generalised fractional Sobolev spaces W qs, p. In this article, we show that the Bourgain …

We introduce a large class of concentrated p-Lévy integrable functions approximating the
unity, which serves as the core tool from which we provide a nonlocal characterization of the …

We investigate the best constants for the regional fractional $ p $-Poincaré inequality and
the fractional $ p $-Poincaré inequality in cylindrical domains. For the special case $ p= 2 …

We show that the Bourgain-Brezis-Mironescu formula, regarding the limits of Gagliardo-type
seminorms as $ s\to 1-$, holds for Triebel-Lizorkin spaces defined in arbitrary domains. This …

We set up a general framework tailor-made to solve complement value problems governed
by symmetric nonlinear integrodifferential $ p $-L\'evy operators. A prototypical example of …

Abstract Let\(\{\rho _\nu\} _ {\nu\in (0,\nu _0)}\) with\(\nu _0\in (0,\infty)\) be a\(\nu _0\)-radial
decreasing approximation of the identity on\(\mathbb {R}^ n\),\(X (\mathbb {R}^ n)\) a ball …

In this work we analyze the behavior of truncated functionals as\begin {equation*}\int_
{\mathbb {R}^ N}\int_ {B (x,\delta)} G\left (\frac {| u (x)-u (y)|}{| xy|^{s}}\right)\frac {dydx}{| xy …