Abstract
In this paper, the Kantorovich operators $$K_n, n\in \mathbb {N}$$ are shown to be uniformly bounded in Morrey spaces on the closed interval [0, 1]. Also an upper estimate is obtained for the difference $$K_n(f)-f$$ 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.
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