The Helmholtz decomposition of weightedLq-spaces for Muckenhoupt weights
✍ Scribed by Andreas Fröhlich
- Book ID
- 105629427
- Publisher
- Springer-Verlag
- Year
- 2000
- Tongue
- German
- Weight
- 333 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0430-3202
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📜 SIMILAR VOLUMES
## Communicated by M. Lachowicz Let f ∈ L 2,-l (R 3 ), where We prove the decomposition f =-∇u+g, with g divergence free and u is a solution to the problem in R 3 Since f, u, g are defined in R 3 we need a sufficiently fast decay of these functions as |x|→∞.
## Abstract This paper deals with atomic decompositions in spaces of type __B^s^~p,q~__ (ℝ^__n__^ , __w__), __F^s^~p,q~__ (ℝ^__n__^ , __w__), 0 < __p__ < ∞, 0 < __q__ ≤ ∞, __s__ ∈ ℝ, where the weight function __w__ belongs to some Muckenhoupt class __A~r~__. In particular, we consider the weight fu
## Abstract We study in detail Hodge–Helmholtz decompositions in nonsmooth exterior domains Ω⊂ℝ^__N__^ filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms of rank __q__ belonging to the weighted L^2^‐space L~__s__~^2, __q__^(Ω), __s__∈ℝ, into ir