Boundedness for the commutator of convolution operator
The author considers the operators which are defined as follows: \[ (T_{b,m}f)(x) = \int_{\mathbb{R}} [b(x)-b(y)]^{m}\frac{\Omega(x-y)}{|x-y|^{n}}f(y) dy, \] and the corresponding maximal operator of the form \[ (T_{b,m}^{\ast}f)(x) = \sup_{\varepsilon>0} \left|\int_{|x-y|>\varepsilon} [b(x)-b(y)]^{m}\frac{\Omega(x-y)}{|x-y|^{n}}f(y) dy \right|. \] The boundedness of these operators is considered in the homogeneous Herz space, which is a generalization of the weighted Lebesgue spaces with power weight.
scientific article; zbMATH DE number 1915769
scientific article