Denseness of the spaces $Φ_V$ of Lizorkin type in the mixed $L^{p̅}(ℝ^n)$-spaces
Studia Mathematica, Tome 113 (1995) no. 3, pp. 199-210
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
The spaces Φ_V(ℝ^{n}) are defined to consist of Schwartz test functions φ such that the Fourier transform φ̂ and all its derivatives vanish on a given closed set V ⊂ ℝ^{n}. Under the only assumption that m(V) = 0 it is shown that Φ_V is dense in $C_0(ℝ^{n})$ and in the space $L^{p̅}(ℝ^n)$ with the mixed norm, for $1/p̅$ in a certain pyramid. The result on the denseness for arbitrary $p̅ = (p_1,..., p_n)$, 1 p_k ∞, k = 1,...,n,$ is proved for so-called quasibroken sets V.
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author = {Stefan Samko},
title = {Denseness of the spaces $\ensuremath{\Phi}_V$ of {Lizorkin} type in the mixed $L^{p̅}(\ensuremath{\mathbb{R}}^n)$-spaces},
journal = {Studia Mathematica},
pages = {199--210},
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Stefan Samko. Denseness of the spaces $Φ_V$ of Lizorkin type in the mixed $L^{p̅}(ℝ^n)$-spaces. Studia Mathematica, Tome 113 (1995) no. 3, pp. 199-210. doi: 10.4064/sm-113-3-199-210
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