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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 ...
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 ...
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 ...
A synthesis of a 1/f process via Sobolev spaces and fractional integration
(Institute of Electrical and Electronics Engineers, 2005-12)
We provide an almost sure convergent expansion of a process with power law of fractional order by means of some known theorems from harmonic analysis and simple probability theory results.
On the boundedness of generalized Cesaro operators on Sobolev spaces
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2014)
Function spaces of coercivity for the fractional Laplacian in spaces of homogeneous type
(Duke University Press, 2019-05)
We combine dyadic analysis through Haar type wavelets defined on Christ´s families of generalized cubes, and Lax-Milgram theorem, in order to prove existence of Green´s functions for fractional Laplacians on some function ...
Funciones de Sobolev y Besov en espacios métricos
(2015-03-09)
En el contexto abstracto de espacios métricos con medida varios autores han considerado espacios de funciones de regularidad tipo Lipschitz o Besov con orden de suavidad alfa menor a uno. Para el extremo alfa igual a uno, ...
Eigenvalues and minimizers for a non-standard growth non-local operator
(Academic Press Inc Elsevier Science, 2020-04)
In this article we study eigenvalues and minimizers of a fractional non-standard growth problem. We prove several properties on these quantities and their corresponding eigenfunctions.