Geodesic
Multipliers in weighted Sobolev spaces
Sbornik. Mathematics, Tome 196 (2005) no. 8, pp. 1109-1136 
L. K. Kusainova. Multipliers in weighted Sobolev spaces. Sbornik. Mathematics, Tome 196 (2005) no. 8, pp. 1109-1136. http://geodesic.mathdoc.fr/item/SM_2005_196_8_a1/
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     author = {L. K. Kusainova},
     title = {Multipliers in weighted {Sobolev} spaces},
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     volume = {196},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_8_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X_1$ and $X_2$ be a pair of Banach spaces of functions in $\Omega\subset\mathbb R^n$. A multiplier from $X_1$ into $X_2$ is a function $\gamma$ on $\Omega$ such that $\gamma X_1=\{\gamma f,\,f\in X_1\}\subset X_2$. By the norm $\|\gamma\|=\|\gamma\|_{M(X_1\to X_2)}$ one means the norm of the operator $T(u)=\gamma u$, $u\in X_1$. Conditions ensuring that a function $\gamma$ belongs to the multiplier classes $M(W_1\to W_2)$ and $M(W\to L)$ are found, where $W$ and $L$ are Sobolev and Lebesgue weighted spaces, respectively. Estimates of the norms of multipliers free from capacity characteristics are found. Special local maximal operators are introduced and significantly used.

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