Título inglés |
Regular mappings between dimensions |
Título español |
Aplicaciones regulares entre dimensiones. |
Autor/es |
David, Guy ; Semmes, Stephen |
Organización |
Univ. París Sud Orsay, París, Francia |
Revista |
0214-1493 |
Publicación |
2000, 44 (2): 369-417, 33 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
The notions of Lipschitz and bilipschitz mappings provide classes of mappings connected to the geometry of metric spaces in certain ways. A notion between these two is given by regular mappings (reviewed in Section 1), in which some non-bilipschitz behavior is allowed, but with limitations on this, and in a quantitative way. In this paper we look at a class of mappings called (s, t)-regular mappings. These mappings are the same as ordinary regular mappings when s = t, but otherwise they behave somewhat like
projections. In particular, they can map sets with Hausdorff dimension s to sets of Hausdorff dimension t. We mostly consider the case of mappings between Euclidean spaces, and show in particular
that if f : Rs → Rn is an (s, t)-regular mapping, then for each ball B in Rs there is a linear mapping λ: Rs → Rs−t and a
subset E of B of substantial measure such that the pair (f, λ) is
bilipschitz on E. We also compare these mappings in comparison with “nonlinear quotient mappings” from [6]. |
Clasificación UNESCO |
121005 |
Palabras clave español |
Aplicación lipschitziana ; Espacio topológico regular ; Integrales singulares |
Código MathReviews |
MR1800814 |
Acceso al artículo completo |