Results 41 to 50 of about 191 (143)
Capacities in metric spaces [PDF]
We discuss the potential theory related to variational capacity and the Sobolev capacity on metric measure spaces. We prove our results within the axiomatic framework.GR-TRAMS Classification : Primary 46E35; Secondary 32U20 ...
Gol'dshtein, Vladimir, Troyanov, Marc
core +1 more source
Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz‐Sobolev embeddings
Journal of Function Spaces, Volume 3, Issue 2, Page 183-208, 2005., 2005 Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x ∈ Ω ⊂ ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A = Lφ,E, B = Lψ,E, giving some optimal (or rather sharp) relations between ...
Evgeniy Pustylnik, Lech Maligranda
wiley +1 more source
Domains of pseudo‐differential operators: a case for the Triebel‐Lizorkin spaces
Journal of Function Spaces, Volume 3, Issue 3, Page 263-286, 2005., 2005 The main result is that every pseudo‐differential operator of type 1, 1 and order d is continuous from the Triebel‐Lizorkin space Fp,1d to Lp, 1 ≤ p≺∞, and that this is optimal within the Besov and Triebel‐Lizorkin scales. The proof also leads to the known continuity for s≻d, while for all real s the sufficiency of Hörmander′s condition on the twisted ...
Jon Johnsen, Victor Burenkov
wiley +1 more source
Box dimension, oscillation and smoothness in function spaces
Journal of Function Spaces, Volume 3, Issue 3, Page 287-320, 2005., 2005 The aim of this paper is twofold. First we relate upper and lower box dimensions with oscillation spaces, and we develop embeddings or inclusions between oscillation spaces and Besov spaces. Secondly, given a point in the (1p, s)‐plane we determine maximal and minimal values for the upper box dimension (also the maximal value for lower box dimension ...
Abel Carvalho, Hans Triebel
wiley +1 more source
Generalized homogeneous Besov spaces and their applications [PDF]
, 2012 2010 Mathematics Subject Classification: Primary 35L05. Secondary 46E35, 35J25, 22E30.In this paper we define the homogeneous Besov spaces associated with the Dunkl operators on R^d, and we give a complete analysis on these spaces and same ...
Mejjaoli, Hatem
core
Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I [PDF]
, 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
core +1 more source
Generalized versus classical normal derivative
, 2023 Given a bounded domain with Lipschitz boundary, the general Green formula permits to justify that the weak solutions of a Neumann elliptic problem satisfy the Neumann boundary condition in a weak sense.
MOTREANU, Viorica V. +3 more
core +1 more source
Sobolev extension in a simple case
Advanced Nonlinear StudiesIn this paper, we establish the existence of a bounded, linear extension operator T:L2,p(E)→L2,p(R2) $T :{L}^{2,p}\left(E\right)\to {L}^{2,p}\left({\mathbb{R}}^{2}\right)$ when 1 < p < 2 and E is a finite subset of R2 ${\mathbb{R}}^{2}$ contained in a ...
Drake Marjorie +3 more
doaj +1 more source
Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces
Open Mathematics, 2017 In Hörmander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions.
Los Valerii, Murach Aleksandr
doaj +1 more source
Hardy–Adams Inequalities on ℍ2 × ℝn-2
Advanced Nonlinear Studies, 2021 Let ℍ2{\mathbb{H}^{2}} be the hyperbolic space of dimension 2. Denote by Mn=ℍ2×ℝn-2{M^{n}=\mathbb{H}^{2}\times\mathbb{R}^{n-2}} the product manifold of ℍ2{\mathbb{H}^{2}} and ℝn-2(n≥3){\mathbb{R}^{n-2}(n\geq 3)}.
Ma Xing, Wang Xumin, Yang Qiaohua
doaj +1 more source