Geodesic
Of Volterra operators in the scale $L_p[0,1]$ $(1\leqslant p\leqslant\infty)$
Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 725-748

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In this article a method of a priori estimates is used to solve an integro-differential equation and to substantially strengthen previously obtained sufficient conditions for the operator $\mathscr Kf=i\int_0^xk(x,t)f(t)\,dt$ to be similar to the operator $\mathscr Tf=i\int_0^xf(t)\,dt$ in the scale $L_p[0,1]$. Criteria for the similarity of $\mathscr K$ to $\mathscr T$ are found for a wide class of kernels which depend on a difference. Bibliography: 17 titles. 
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     author = {M. M. Malamud and \`E. R. Tsekanovskii},
     title = {Of {Volterra} operators in the scale $L_p[0,1]$ $(1\leqslant p\leqslant\infty)$},
     journal = {Izvestiya. Mathematics },
     pages = {725--748},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a2/}
}
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M. M. Malamud; È. R. Tsekanovskii. Of Volterra operators in the scale $L_p[0,1]$ $(1\leqslant p\leqslant\infty)$. Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 725-748. http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a2/