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Abstract The paper provides a detailed study of crucial inequalities for smoothness and interpolation characteristics in rearrangement invariant Banach function spaces. We present a unified approach based on Holmstedt formulas to obtain these estimates. As examples, we derive new inequalities for moduli of smoothness and K -functionals in various Lorentz spaces.
Гогатишвили et al. (Mon,) studied this question.
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