Uniform Boundedness of Sz´ asz–Mirakjan–Kantorovich Operators in Morrey Spaces with Variable Exponents

Abstract

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 local exponent is global log-Hölder continuous.