Multidimensional integral operators with homogeneous kernels of compact type and multiplicatively weakly oscillating coefficients

Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces

“…The following theorem is a generalization of some results obtained for operators with homogeneous kernels (see [1], [3]). Theorem 1.…”

“…In their papers assumptions of invariance under diagonal action of group SO(n) were imposed and considerably used in addition to homogeneity conditions. New broad class of operators with kernels of compact type including the set of SO(n)-invariant kernels was introduced and investigated in [3]. In [4] the results of [3] on boundedness and Fredholm property are expanded to the case of operators with anisotropically homogeneous kernels.…”

“…New broad class of operators with kernels of compact type including the set of SO(n)-invariant kernels was introduced and investigated in [3]. In [4] the results of [3] on boundedness and Fredholm property are expanded to the case of operators with anisotropically homogeneous kernels. The purpose of the present paper is to extend results related to boundedness and invertibility to the case of weighted L p -spaces.…”

FREDHOLM PROPERTY OF COMPOSITE TWO-DIMENSIONAL INTEGRAL OPERATORS WITH HOMOGENEOUS SINGULAR-TYPE KERNELS IN pL SPACE

“…Кроме условий однородности в данных работах на ядра накладывались и существенно использовались условия инвариантности относительно диагонального действия группы ортогональных преобразований SO(n). В [3,4] рассматривались классы ядер компактного и сингулярного типа, включающие в себя SO(n)-инвариантные ядра, а также методами теории операторов локального [5] и билокального типа [6] исследовалась разрешимость операторов с однородными ядрами и переменными коэффициентами. Топологические свойства пространств обратимых и фредгольмовых операторов из этого класса изучались в [7].…”