Geodesic
On the vanishing of the symbol of a convolution integral operator
Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 239-253 
V. D. Stepanov. On the vanishing of the symbol of a convolution integral operator. Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 239-253. http://geodesic.mathdoc.fr/item/SM_1985_51_1_a14/
@article{SM_1985_51_1_a14,
     author = {V. D. Stepanov},
     title = {On the vanishing of the symbol of a~convolution integral operator},
     journal = {Sbornik. Mathematics},
     pages = {239--253},
     year = {1985},
     volume = {51},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_51_1_a14/}
}
TY  - JOUR
AU  - V. D. Stepanov
TI  - On the vanishing of the symbol of a convolution integral operator
JO  - Sbornik. Mathematics
PY  - 1985
SP  - 239
EP  - 253
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1985_51_1_a14/
LA  - en
ID  - SM_1985_51_1_a14
ER  - 
%0 Journal Article
%A V. D. Stepanov
%T On the vanishing of the symbol of a convolution integral operator
%J Sbornik. Mathematics
%D 1985
%P 239-253
%V 51
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1985_51_1_a14/
%G en
%F SM_1985_51_1_a14

Voir la notice de l'article provenant de la source Math-Net.Ru

The class $\operatorname{Int}(p,p)$ of kernels of convolution integral operators is defined, and a criterion for a measurable function to belong to $\operatorname{Int}(p,p)$ is given. The question of the behavior of the Fourier transform of a kernel (the symbol) in $\operatorname{Int}(2,2)$ is considered, and it is shown that in the sense of order the symbol can vanish at infinity in an arbitrarily slow manner, and more slowly than any power in the mean. Bibliography: 6 titles.

[1] Stepanov V. D., “Ob odnoi zadache dlya integralnykh operatorov svertki”, Matem. sb., 120(162) (1983), 216–226 | Zbl

[2] Khërmander L., Otsenki dlya operatorov, invariantnykh otnositelno sdviga, IL, M., 1962

[3] Halmos P. R., Sunder V. S., Bounded integral operators on $L^2$ spaces, Springer-Verlag, Berlin a.o., 1978 | MR

[4] Bari N. K., Trigonometricheskie ryady, Fizmatlit, M., 1961 | MR

[5] Zigmund A., Trigonometricheskie ryady, T. I, Mir, M., 1965 | MR

[6] Erdeii A., Asimptoticheskie razlozheniya, Fizmatlit, M., 1962