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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
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Weighted Sobolev Spaces on Metric Measure Spaces [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2015 We investigate weighted Sobolev spaces on metric measure spaces $(X,d,m)$. Denoting by $\rho$ the weight function, we compare the space $W^{1,p}(X,d,\rho m)$ (which always concides with the closure $H^{1,p}(X,d,\rho m)$ of Lipschitz functions) with the ...
Ambrosio, Luigi +2 more
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Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I [PDF]
Acta Applicandae Mathematica, 2004 36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this ...
Pestana, Domingo +3 more
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Weighted Variable Exponent Sobolev spaces on metric measure spaces [PDF]
Moroccan Journal of Pure and Applied Analysis, 2018 In this article we define the weighted variable exponent-Sobolev spaces on arbitrary metric spaces, with finite diameter and equipped with finite, positive Borel regular outer measure.
Hassib Moulay Cherif, Akdim Youssef
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A new approach to weighted Sobolev spaces. [PDF]
Mon Hefte MathAbstract 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.
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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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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.
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Lupaş-type inequality and applications to Markov-type inequalities in weighted Sobolev spaces
Bulletin of Mathematical Sciences, 2021 Weighted Sobolev spaces play a main role in the study of Sobolev orthogonal polynomials. In particular, analytic properties of such polynomials have been extensively studied, mainly focused on their asymptotic behavior and the location of their zeros. On
Francisco Marcellán +1 more
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Weighted critical exponents of Sobolev-type embeddings for radial functions
Advanced Nonlinear Studies, 2022 In this article, we prove the upper weighted critical exponents for some embeddings from weighted Sobolev spaces of radial functions into weighted Lebesgue spaces. We also consider the lower critical exponent for certain embedding.
Su Jiabao, Wang Cong
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Fredholm property of regular hypoelliptic operators on the scales of multianisotropic spaces [PDF]
ITM Web of Conferences, 2022 This paper studies the Fredholm properties for a class of regular hypoelliptic operators. We establish necessary and sufficient conditions for a priori estimates for differential operators acting in multianisotropic Sobolev spaces in Rn.
Tumanyan Ani
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