Geodesic
Multidimensional Integral Operators with Homogeneous Kernels of Compact Type and Multiplicatively Weakly Oscillating Coefficients
Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 704-720

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

In the space $L_p(\mathbb R^n)$, $1$, we consider a new class of integral operators with kernels homogeneous of degree $-n$, which includes the class of operators with homogeneous $SO(n)$-invariant kernels; we study the Banach algebra generated by such operators with multiplicatively weakly oscillating coefficients. For operators from this algebra, we define a symbol in terms of which we formulate a Fredholm property criterion and derive a formula for calculating the index. An important stage in obtaining these results is the establishment of the relationship between the operators of the class under study and the operators of one-dimensional convolution with weakly oscillating compact coefficients.
Keywords: multidimensional integral operator, operators with multiplicatively weakly oscillating coefficients, homogeneous kernel, convolution operator, the space $L_p(\mathbb R^n)$. 
@article{MZM_2010_87_5_a5,
     author = {V. M. Deundyak},
     title = {Multidimensional {Integral} {Operators} with {Homogeneous} {Kernels} of {Compact} {Type} and {Multiplicatively} {Weakly} {Oscillating}  {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {704--720},
     publisher = {mathdoc},
     volume = {87},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a5/}
}
TY  - JOUR
AU  - V. M. Deundyak
TI  - Multidimensional Integral Operators with Homogeneous Kernels of Compact Type and Multiplicatively Weakly Oscillating  Coefficients
JO  - Matematičeskie zametki
PY  - 2010
SP  - 704
EP  - 720
VL  - 87
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a5/
LA  - ru
ID  - MZM_2010_87_5_a5
ER  - 
%0 Journal Article
%A V. M. Deundyak
%T Multidimensional Integral Operators with Homogeneous Kernels of Compact Type and Multiplicatively Weakly Oscillating  Coefficients
%J Matematičeskie zametki
%D 2010
%P 704-720
%V 87
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a5/
%G ru
%F MZM_2010_87_5_a5
V. M. Deundyak. Multidimensional Integral Operators with Homogeneous Kernels of Compact Type and Multiplicatively Weakly Oscillating  Coefficients. Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 704-720. http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a5/