ULYANOV INEQUALITIES FOR THE MIXED MODULI OF SMOOTHNESS IN MIXED METRICS

Abstract

In this paper, mixed moduli of smoothness of functions of two variables are studied. We prove Ulyanov-type inequalities between mixed moduli of smoothness of positive orders in different metrics. Estimates for the mixed moduli of smoothness of the derivative of a function are also obtained in terms of the mixed moduli of smoothness of the function itself.