On one inequality for the moduli of continuity of fractional order generated by semigroups of operators

Abstract

A new inequality for the moduli of continuity of fractional order generated by semigroups of operators is obtained. This inequality implies a generalization of the well-known statement that there exists an $α$-majorant, which is not a modulus of continuity of order $α$ generated by a semigroup of operators, to the case of noninteger values of $α$.