The boundedness and the Fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients
In the space \(L_p(\mathbb R^n), \, 1 < p < \infty\), a new class of integral operators with anisotropically homogeneous kernels is studied. Sufficient conditions are obtained for the boundedness of operators from this class. Further, the authors consider the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type and multiplicative-slowly oscillating coefficients. Moreover, relationships are established between this algebra and multidimensional convolution operators, and a symbolic calculus is constructed for it. Also, necessary and sufficient conditions are obtained for the Fredholm property of operators from this algebra.
scientific article; zbMATH DE number 6108825