Maximal inequalities for dual Sobolev spaces $W^{-1,p}$ and applications to interpolation
نویسندگان
چکیده
منابع مشابه
Maximal inequalities for dual Sobolev spaces W − 1 , p and applications to interpolation
We firstly describe a maximal inequality for dual Sobolev spaces W−1,p. This one corresponds to a “Sobolev version” of usual properties of the Hardy-Littlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one seems to be new and we develop arguments in the general framework of Riemannian manifold. Then we present an application to obtain interpolation results for Sobol...
متن کاملInterpolation Inequalities in Weighted Sobolev Spaces
In this paper we prove some interpolation inequalities between functions and their derivatives in the class of weighted Sobolev spaces defined on unbounded open subset Ω ⊂ Rn .
متن کاملPiecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications
We develop a constructive piecewise polynomial approximation theory in 1 weighted Sobolev spaces with Muckenhoupt weights for any polynomial degree. The 2 main ingredients to derive optimal error estimates for an averaged Taylor polynomial 3 are a suitable weighted Poincaré inequality, a cancellation property and a simple 4 induction argument. We also construct a quasi-interpolation operator, b...
متن کاملRadial Basis Function Interpolation in Sobolev Spaces and Its Applications
In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H(Ω) (k ≥ 1). With a special kind of radial basis function, we construct a basis in H(Ω) and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density. Mathematics subject classification: 41...
متن کاملReal interpolation of Sobolev spaces
We prove that W 1 p is a real interpolation space between W 1 p1 and W 1 p2 for p > q0 and 1 ≤ p1 < p < p2 ≤ ∞ on some classes of manifolds and general metric spaces, where q0 depends on our hypotheses.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2009
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2009.v16.n5.a2