Geodesic
Toeplitz--Schur multipliers of $S_p(L^2(G))$ for $p1$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 5-19

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We study Toeplitz–Schur multipliers of Schatten–von Neumann class $S_p$ for $0$. We describe all functions $F$ on an arbitrary commutative locally compact group $G$ satisfying the following condition: for any integral operator in $S_p$ with kernel function $k(x,y)$, the kernel function $F(x-y)k(x)k(y)$ determines also an integral operator in $S_p$. 
@article{ZNSL_2001_282_a0,
     author = {A. B. Aleksandrov},
     title = {Toeplitz--Schur multipliers of $S_p(L^2(G))$ for $p<1$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--19},
     publisher = {mathdoc},
     volume = {282},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a0/}
}
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A. B. Aleksandrov. Toeplitz--Schur multipliers of $S_p(L^2(G))$ for $p<1$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 5-19. http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a0/