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The paper provides a detailed study of crucial inequalities for smoothnessand interpolation characteristics in rearrangement invariant Banach functionspaces. We present a unified approach based on Holmstedt formulas to obtainthese estimates. As examples, we derive new inequalities for moduli ofsmoothness and K-functionals in various Lorentz spaces.

A unified approach to inequalities for K-functionals and moduli of smoothness