The Szász–Mirakjan–Kantorovich operators and the Baskakov–Kantorovich operators are shown to be controlled by the Hardy–Littlewood maximal operator. The Szász–Mirakjan–Kantorovich operators and the Baskakov–Kantorovich operators turn out to be uniformly bounded in Lebesgue spaces and Morrey spaces with variable exponents when the integral exponent is global log-Hölder continuous.