Uniform Boundedness Of Some Approximation Operators In Morrey Spaces With Variable Exponents

In recent years,scholars have continued to break the approximation operator in spaces with constant exponents.With the wide application of function spaces with variable exponent in hydrodynamics,partial differential equation,image restoration and other aspects,some scholars began to study the approximation operator in Lebesgue spaces with variable exponents.Affected by these studies,in this dissertation,controlling some approximation operators by the Hardy-Littlewood maximal operator,we obtain the uniform boundedness of them in Morrey spaces with variable exponents via.First,we obtain that the Kantorovich polynomial operators are uniformly bounded in Morrey s-paces with variable exponents.Second,we first prove that the Szasz-Mirakjan-Kantorovich opera-tors can be controlled by the Hardy-Littlewood maximal operator.Then,by the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces with variable exponents,we prove that the Szasz-Mirakjan-Kantorovich operators are uniformly bounded in Morrey spaces with variable exponents.Fi-nally,we obtain the Baskakov-Kantorovich operators are also uniformly bounded in Morrey spaces with variable exponents.