On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients

In this paper, we study the Banach algebra $\mathfrak B$ generated by multidimensional integral operators whose kernels are homogeneous functions of degree $(-n)$ invariant with respect to the rotation group $SO(n)$ and by the operators of multiplication by radial weakly oscillating functions. A symbolic calculus is developed for the algebra $\mathfrak B$. The Fredholm property and the formula for calculating the index are described in terms of this calculus.