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Fractional order Orlicz-Sobolev spaces
(Academic Press Inc Elsevier Science, 2019-04)
In this paper we define the fractional order Orlicz-Sobolev spaces, and prove its convergence to the classical Orlicz-Sobolev spaces when the fractional parameter s↑1 in the spirit of the celebrated result of Bourgain-Br ...
Fractional Sobolev spaces with variable exponents and fractional p(X)-Laplacians
(Univ Szeged, 2017-11)
In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we ...
Magnetic fractional order orlicz-sobolev spaces
(Polish Academy of Sciences. Institute of Mathematics, 2021-01)
We define the notion of nonlocal magnetic Sobolev spaces with nonstandard growth for Lipschitz magnetic fields. In this context we prove a Bourgain-Brezis- Mironescu type formula for functions in this space as well as for ...
Maz'ya-Shaposhnikova formula in magnetic fractional Orlicz–Sobolev spaces
(IOS Press, 2022)
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 ...
Improved Poincaré inequalities in fractional Sobolev spaces
(Suomalainen Tiedeakatemia, 2018-03)
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.
On Best Constants for Limiting Embeddings of Fractional Sobolev Spaces
(Advanced Nonlinear Studies, IncSan AntonioEUA, 2010)
A note on homogeneous Sobolev spaces of fractional order
(Springer Heidelberg, 2019-08)
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 ...
A Hölder infinity Laplacian obtained as limit of Orlicz fractional Laplacians
(Springer, 2022-05)
This paper concerns the study of the asymptotic behavior of the solutions to a family of fractional type problems on a bounded domain, satisfying homogeneous Dirichlet boundary conditions. The family of differential operators ...
Bessel Potentials in Ahlfors Regular Metric Spaces
(Springer, 2016-08)
In this paper we introduce Bessel potentials and the Sobolev potential spaces resulting from them in the context of Ahlfors regular metric spaces. The Bessel kernel is defined using a Coifman type approximation of the ...
Asymptotic Behaviours in Fractional Orlicz–Sobolev Spaces on Carnot Groups
(Springer, 2020-03)
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 ...