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Weighted Variable Sobolev Spaces and Capacity [PDF]

Journal of Function Spaces and Applications, 2012
We define weighted variable Sobolev capacity and discuss properties of capacity in the space 𝑊1,𝑝(⋅)(ℝ𝑛,𝑤). We investigate the role of capacity in the pointwise definition of functions in this space if the Hardy-Littlewood maximal operator is bounded on ...
Ismail Aydin
doaj   +2 more sources

Weighted Sobolev spaces on metric measure spaces [PDF]

Journal für die reine und angewandte Mathematik (Crelles Journal), 2016
Abstract We investigate weighted Sobolev spaces on metric measure spaces ( X , d ...
Ambrosio, Luigi, Pinamonti, Andrea, Speight, Gareth   +2 more
openaire   +6 more sources

A new approach to weighted Sobolev spaces. [PDF]

Mon Hefte Math
Abstract We present in this paper a new way to define weighted Sobolev spaces when the weight functions are arbitrary small. This new approach can replace the old one consisting in modifying the domain by removing the set of points where at least one of the weight functions is very small.
Kebiche D.
europepmc   +7 more sources

Multipliers in weighted Sobolev spaces on the axis [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
This work establishes necessary and sufficient conditions for the boundedness of one variable differential operator acting from a weighted Sobolev space Wlp,v to a weighted Lebesgue space on the positive real half line.
A. Myrzagaliyeva
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On the approximation of solutions of one singular differential equation on the axis [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
In this paper we study the problem of the best approximation by linear methods of solutions to one Triebel-type equation. This problem was solved by using estimates of the linear widths of the unit ball in corresponding spaces of differentiable ...
A.S. Kassym, L.K. Kussainova
doaj   +3 more sources

Anisotropic Sobolev Spaces with Weights

Tokyo Journal of Mathematics, 2023
We study Sobolev spaces with weights in the half-space $\mathbb{R}^{N+1}_+=\{(x,y): x \in \mathbb{R}^N, y>0\}$, adapted to the singular elliptic operators \begin{equation*} \mathcal L =y^{ _1} _{x} +y^{ _2}\left(D_{yy}+\frac{c}{y}D_y -\frac{b}{y^2}\right). \end{equation*}
Metafune G., Negro L., Spina C.
openaire   +3 more sources

On a New Parabolic Sobolev Embedding Map

Moroccan Journal of Pure and Applied Analysis, 2023
The purpose of the present article is to provide a new parabolic Sobolev embedding map between a parabolic weighted Sobolev space and the space of square-integrable functions on a cylinder. Furthermore, the embedding constant is furnished explicitly.
El Aidi Mohammed
doaj   +1 more source

Vlasov-Poisson equation in weighted Sobolev space $W^{m, p}(w)$

Cubo, 2022
In this paper, we are concerned about the well-posedness of Vlasov-Poisson equation near vaccum in weighted Sobolev space $W^{m, p}(w).$ The most difficult part comes from estimates of the electronic term $\nabla_{x}\phi.$ To overcome this difficulty,
Cong He, Jingchun Chen
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Boundedness of One Class of Integral Operators from Second Order Weighted Sobolev Space to Weighted Lebesgue Space

Journal of Function Spaces, 2022
In the paper, for a certain class of Hardy operators with kernels, we consider the problem of their boundedness from a second order weighted Sobolev space to a weighted Lebesgue space.
Aigerim Kalybay
doaj   +1 more source

Solvability of a system of integral equations in two variables in the weighted Sobolev space $W^{1,1}_\omega(a,b)$ using a generalized measure of noncompactness

Nonlinear Analysis, 2022
In this paper, we deal with the existence of solutions for a coupled system of integral equations in the Cartesian product of weighted Sobolev spaces E = Wω1,1 (a,b) x Wω1,1 (a,b).
Taqi A.M. Shatnawi, Ahmed Boudaoui, Wasfi Shatanawi, Noura Laksaci   +3 more
doaj   +1 more source