On Whitney-type extension theorems on Banach spaces for \(C^{1, \omega}, C^{1,+}, C_{\operatorname{loc}}^{1, +}\), and \(C_{\operatorname{B}}^{1, +}\)-smooth functions
From MaRDI portal
Publication:6140910
DOI10.1016/j.jmaa.2023.127976arXiv2305.19995OpenAlexW4388840937MaRDI QIDQ6140910
Luděk Zajíček, Václav Kryštof, Michal Johanis
Publication date: 2 January 2024
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2305.19995
Whitney extension theoremsuper-reflexive spacesquasiconvex setsfunctions with a uniformly continuous derivative
Normed linear spaces and Banach spaces; Banach lattices (46Bxx) Functions of several variables (26Bxx) Calculus on manifolds; nonlinear operators (58Cxx)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Smooth extension of functions on a certain class of non-separable Banach spaces
- Semiconcave functions, Hamilton-Jacobi equations, and optimal control
- Extension of uniformly continuous transformations and hyperconvex metric spaces
- Étude de quelques algèbres tayloriennes
- Whitney's extension problem for \(C^m\)
- Characterizing metric spaces whose hyperspaces are absolute neighborhood retracts
- Norms with locally Lipschitzian derivatives
- Smooth functions on \(c_0\)
- The Whitney problem of existence of a linear extension operator
- Explicit formulas for \(C^{1,1}\) and \(C_{\operatorname{conv}}^{1, \omega}\) extensions of 1-jets in Hilbert and superreflexive spaces
- Differentiable functions on Banach spaces with Lipschitz derivatives
- On mappings of bounded variation
- \(C^{1, \omega }\) extension formulas for $1$-jets on Hilbert spaces
- Polynomial algebras and smooth functions in Banach spaces
- Minimal Lipschitz extensions to differentiable functions defined on a Hilbert space
- Whitney’s extension problem for multivariate 𝐶^{1,𝜔}-functions
- C 1,ω (·) -regularity and Lipschitz-like properties of subdifferential
- Uniformly smooth partitions of unity on superreflexive Banach spaces
- Relatively and inner uniform domains
- Generalized versions of Ilmanen lemma: Insertion of $ C^{1,\omega} $ or $ C^{1,\omega}_{{\rm loc}} $ functions
- Further generalized versions of Ilmanen's lemma on insertion of $C^{1,\omega}$ or $C^{1,\omega}_{\text{\rm loc}}$ functions
- Functions on a convex set which are both $\omega$-semiconvex and $\omega$-semiconcave
- Smooth analysis in Banach spaces
- Methods of Geometric Analysis in Extension and Trace Problems