Properties of the Sobolev space $H_k^{s,s^{\prime }}$

Henryk Kołakowski

Properties of the Sobolev space

H_{k}^{s, s^{'}}

Henryk Kołakowski

Annales Polonici Mathematici, Tome 72 (1999), p. 199-209 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let n ≥ 2 and $H_{k}^{s, s^{'}} = u \in S^{'} (ℝ^{n}) : ∥ u ∥_{s, s^{'}} < \infty$ , where $∥ u ∥ ²_{s, s^{'}} = {(2 π)}^{- n} \int {(1 + | ξ | ²)}^{s} (1 + | ξ^{'} {| ²)}^{s^{'}} | F u (ξ) | ² d ξ$ , $F u (ξ) = \int e^{- i x ξ} u (x) d x$ , $ξ^{'} \in ℝ^{k}$ , k < n. We prove that for some s,s’ the space $H_{k}^{s, s^{'}}$ is a multiplicative algebra.

Publié le : 1999-01-01

Zbl 0945.46016

EUDML-ID : urn:eudml:doc:262677

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     author = {Henryk Ko\l akowski},
     title = {Properties of the Sobolev space $H\_k^{s,s^{\prime }}$
            },
     journal = {Annales Polonici Mathematici},
     volume = {72},
     year = {1999},
     pages = {199-209},
     zbl = {0945.46016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv71z2p199bwm}
}

Henryk Kołakowski. Properties of the Sobolev space $H_k^{s,s^{\prime }}$
            . Annales Polonici Mathematici, Tome 72 (1999) pp. 199-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv71z2p199bwm/

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