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Interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces
interpolation inequality Landau-Kolmogorov type inequality Variable exponent Lebesgue-Sobolev space maximal function operator
2011/10/26
The author shows the interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces by applying the boundedness of the Hardy-Littlewood maximal operator on L^{p(x)}. As applic...
Algebra properties for Sobolev spaces- Applications to semilinear PDE's on manifolds
Sobolev spaces Riemannian manifold algebra rule paraproducts heat semigroup
2011/9/15
Abstract: In this work, we aim to prove algebra properties for generalized Sobolev spaces $W^{s,p} \cap L^\infty$ on a Riemannian manifold, where $W^{s,p}$ is of Bessel-type $W^{s,p}:=(1+L)^{-s/m}(L^p...
Uniform Estimates of the Prolate Spheroidal Wave Functions and Spectral Approximation in Sobolev Spaces
Uniform Estimates of the Prolate Spheroidal Wave Functions Spectral Approximation Sobolev Spaces
2011/2/22
For fixed c Prolate Spheroidal Wave Functions ψn,c form a basis with remarkable properties
for the space of band-limited functions with bandwith c and have been largely studied and
used after the se...
Polynomial Approximation in Sobolev Spaces on the Unit Sphere and the Unit Ball
Polynomial Sobolev Spaces Unit Sphere Unit Ball
2010/11/18
This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial ap...
In this paper we present a new characterization of Sobolev spaces on Euclidian spaces ($\mathbb{R}^n$). Our characterizing condition is obtained via a quadratic multiscale expression which exploits t...
Global solutions for the generalized Boussinesq equation in low-order Sobolev spaces
Global solutions generalized Boussinesq equation low-order Sobolev spaces
2010/12/14
We show that the Cauchy problem for the defocusing generalized Boussinesq equation utt − uxx + uxxxx − (|u|2ku)xx = 0, k 1, on the real line is globally well-posed in Hs(R) for s > 1W...
Generalized Dunkl-Sobolev Spaces of Exponential Type and Applications
Dunkl operators Dunkl-Bessel-Laplace operator Generalized Dunkl-Sobolev spaces of exponential type Pseudo differential-difference operators Reproducing kernels
2010/1/22
We study the Sobolev spaces of exponential type associated with the Dunkl-Bessel Laplace operator. Some properties including completeness and the imbedding theorem are proved. We next introduce a clas...
A Multiplicative Embedding Inequality in Orlicz-Sobolev Spaces
Orlicz spaces Sobolev embedding theorem Orlicz-Sobolev spaces
2008/7/3
We prove an Orlicz type version of the multiplicative embedding inequality for Sobolev spaces.
$N$-Widths and Average Widths of Besov Classes in the Sobolev Spaces
Besov class $n$-width Sobolev space Average width
2007/12/12
In this paper, we consider the $n$-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov $n$-widths, the linear $n$-widths, the ...
Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices
Kawahara equation Cauchy problem global solution almost conservation law
2007/12/11
We first prove that the Cauchy problem of the Kawahara equation, $\partial_tu+u\partial_xu+\beta\partial_x^3u+\gamma\partial_x^5u=0,$ is locally solvable if the initial data belong to $H^{r}(\bf{R})...
Convergence of cascade algorithms in Sobolev spaces associated with multiviate refinement equations
2007/7/28
专著信息
书名
Convergence of cascade algorithms in Sobolev spaces associated with multiviate refinement equations
语种
英文
撰写或编译
作者
李松
第一作者单位
出版社
Journal of mathematical analysis and applications,257,154-169,2...