Boundedness and Invertibility of Multidimensional Integral Operators with Anisotropically Homogeneous Kernels in Weighted Lp-spaces

In weighted space L-p (R-n, rho), 1 < p < infinity, a new broad class of integral operators with anisotropically homogeneous kernels is investigated. For such operators boundedness theorem is proved. Also the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type is considered. For elements of the algebra symbolic calculation is constructed, the invertibility criterion is obtained in terms of operator symbol.