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BMO and Injectivity of Space Quasiregular Mappings

✍ Scribed by Olli Martio; Vladimir Ryazanov; Matti Vuorinen

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
567 KB
Volume
205
Category
Article
ISSN
0025-584X

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✦ Synopsis

It is shown that if the dilatation tensor Gf of a space quasiregular mapping f belongs lo the space VMO (vanishing mean oscillation), then f is a local homeomorphism. The same is true If the BMO-norm of Gf is small or if Gf is only close to the VMO space in the BMO-norm.

πŸ“œ SIMILAR VOLUMES

Boundedness of Lusin-area and functions
Boundedness of Lusin-area and functions on localized BMO spaces over doubling metric measure spaces
✍ Haibo Lin; Eiichi Nakai; Dachun Yang πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 French βš– 258 KB

Let X be a doubling metric measure space. If X has the δ-annular decay property for some δ ∈ (0, 1], the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the semigroup generated by the Schrâdinger operator, from localized spaces BMO ρ (X ) to