Geodesic
Multipliers on Besov spaces
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 36-50

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It is proved that the characteristic function of a halfepace $\mathbb R_n^+$ is not a multiplier for the pair $(B_{pq}^{1/p}, B_{p\infty}^{1/p})$, $1$, $1$. A necessary and sufficient condition is given for $\chi_E$ to belong to $\in M(B_{p1}^{1/p}\to B_{p\infty}^{1/p})$. 
@article{ZNSL_1984_135_a2,
     author = {A. B. Gulisashvili},
     title = {Multipliers on {Besov} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {36--50},
     publisher = {mathdoc},
     volume = {135},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_135_a2/}
}
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A. B. Gulisashvili. Multipliers on Besov spaces. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 36-50. http://geodesic.mathdoc.fr/item/ZNSL_1984_135_a2/