Denseness of the spaces $Φ_V$ of Lizorkin type in the mixed $L^{p̅}(ℝ^n)$-spaces

• Autorzy: Stefan Samko
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 41A30: Approximation by other special function classes
• 42B99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 113
• Numer: 3
• Strony: 199-210

Daty

wydano

1995

otrzymano

1991-07-26

poprawiono

1994-09-07

Twórcy

autor

Stefan Samko

• Department of Mathematics and Mechanics, Rostov State University, Bol'shaya Sadovaya 105, 344711 Rostov-na-donu, Russia

Bibliografia

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