On the boundedness of singular integral operators from certain classes. II
The boundedness of anisotropic singular integral operators with the domains of definition and ranges in various anisotropic spaces of Banach-valued functions is analyzed from a unified point of view. A number of parameterized classes of sufficient conditions are obtained that are expressed in terms of the approximation D-functional. Our sufficient conditions are weaker then their known counterparts in the same settings. The inhomogeneity of the dependence on certain parameters is revealed. The results obtained are also applicable to nonsingular (in the ordinary sense) integral operators, for example, to potential-type operators. The main results are presented in the style of the Calder´on–Zygmund theory. The approach is based on the study of decompositions of operators and some properties of the related function spaces.