Uniform boundedness of Kantorovich operators in Morrey spaces

In this paper, the Kantorovich operators Kn, n∈ N are shown to be uniformly bounded in Morrey spaces on the closed interval [0, 1]. Also an upper estimate is obtained for the difference Kn(f) - f for functions f of regularity of order 1 measured in Morrey spaces. One of the key tools is the pointwise inequality for the Kantorovich operators and the Hardy–Littlewood maximal operator, which is of interest on its own and can be applied to other problems related to the Kantorovich operators. © 2018, Springer International Publishing AG, part of Springer Nature.