Geodesic
Local square summability of convolutions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part VIII, Tome 73 (1977), pp. 211-216

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Let $\mathscr P(D)$ and $\mathscr R(D)$ be two convolution operators in $\mathbf R^n$ and $K$ be an arbitrary compact subset of $\mathbf R^n$, having interior points. Necessary and sufficient conditions are given for the boundedness and compactness of the ball $\{u:\|\mathscr P(D)u\|_{L^2(\mathbf R^n)}\leqslant1\}$ in the metric of $\|\mathscr R(D)u\|_{L^2(K}$. 
@article{ZNSL_1977_73_a16,
     author = {V. G. Maz'ya},
     title = {Local square summability of convolutions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {211--216},
     publisher = {mathdoc},
     volume = {73},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_73_a16/}
}
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V. G. Maz'ya. Local square summability of convolutions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part VIII, Tome 73 (1977), pp. 211-216. http://geodesic.mathdoc.fr/item/ZNSL_1977_73_a16/