Results 11 to 20 of about 32,440 (193)

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), 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, Pinamonti, Andrea, Speight, Gareth   +2 more
core   +5 more sources

Weighted Sobolev inequality in Musielak–Orlicz space

Journal of Mathematical Analysis and Applications, 2012
Let \(L_{p,q,\beta}(\mathbb{R}^n)\) be the Lebesgue space with continuous variable exponents \(p\), \(q\) satisfying the log-Hölder and log-log-Hölder condition, respectively, defined by means of the quasi-norm \[ \| f\|_{L_{p,q,\beta}(\mathbb{R}^n)}= \text{inf}\{\lambda> 0: \int(1+ |y|)^{\beta(y)}|f(y)/\lambda|^{p(y)}\cdot[\log(e+ |y|)^{\beta(y)}\cdot|
Mizuta, Yoshihiro, Shimomura, Tetsu
openaire   +4 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

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

A density property for fractional weighted Sobolev spaces [PDF]

, 2015
In this paper we show a density property for fractional weighted Sobolev spaces. That is, we prove that any function in a fractional weighted Sobolev space can be approximated by a smooth function with compact support. The additional difficulty in this
Dipierro, Serena, Valdinoci, Enrico
core   +4 more sources

Generalized Weighted Sobolev Spaces and Applications to Sobolev Orthogonal Polynomials I [PDF]

Acta Applicandae Mathematica, 2002
In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory.
Rodríguez, José M., Álvarez, Venancio, Romera, Elena, Pestana, Domingo   +3 more
openaire   +4 more sources

Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications [PDF]

, 2018
We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply ...
Antil, Harbir, Rautenberg, Carlos N.
core   +3 more sources

Geometric ergodicity in a weighted Sobolev space [PDF]

The Annals of Probability, 2020
For a discrete-time Markov chain $\{X(t)\}$ evolving on $\Re^\ell$ with transition kernel $P$, natural, general conditions are developed under which the following are established: 1. The transition kernel $P$ has a purely discrete spectrum, when viewed as a linear operator on a weighted Sobolev space $L_\infty^{v,1}$ of functions with norm, $$ \|f\|_{v,
Devraj, Adithya, Kontoyiannis, Ioannis, Meyn, Sean   +2 more
openaire   +4 more sources

Weighted Sobolev Spaces on Curves

Journal of Approximation Theory, 2002
45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10. MR#: MR1934626 (2003j:46038) Zbl#: Zbl 1019.46026 In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally,
Alvarez, Venancio, Pestana, Domingo, Rodríguez, José M., Romera, Elena   +3 more
openaire   +3 more sources