One generalization of Marchaud inequality onsignsensitive weights

At the proof of a classical Marсhaud inequality for equidistant moduli of continuity of the highest degree the reduction of their definition for arbitrary sign of a step of a finite difference to positive values of this step is used. In case of moduli of continuity with a weight such reduction reduces definitions of moduli of continuity to restriction. Consequently for determination of properties of moduli of continuity with a weight other approach of reasoning is required. Unlike usual weight signsensitive weight allows to consider not only an absolute value of an increment of function, but also a sign of this increment. In the work for metrics with signsensitive weight an analogue of Marchaud inequality on estimation of modulus of continuity of given degree over modulus of continuity of a higher degree is obtained.

modulus of continuity, signsensitive weight, continuous functions, modulus of smoothness, finite differences, Marchaud inequality, classes of functions, embedding theorems