Functions of one variable are considered in the article. The relationships between smoothness moduli in different metrics are established, refining previously known estimates.
moduli of smoothness, metric
1. Potapov M. K. O sootnosheniyah mezhdu modulyami gladkosti v raznyh metrikah / M. K. Potapov, B. V. Simonov, S. Yu. Tihonov // Vestn. Mosk. un-ta. Matem. Mehan. 2009. № 3. S. 17-25. EDN: https://elibrary.ru/MKTYLX
2. Tikhonov S. Ulyanov inequalities and generalized Liouville derivatives / S. Tikhonov, W. Trebels // Proc. Roy. Soc. Edinburgh Sect. A. 2011. 141. No. 1. P. 205-224. DOI: https://doi.org/10.1017/S0308210509001048
3. Tikhonov S. Weak type inequalities for moduli of smoothness: the case of limit value parameters / S. Tikhonov // J. Fourier Anal. Appl. 2010. 16. No. 4. P. 590-608. DOI: https://doi.org/10.1007/s00041-009-9101-1; EDN: https://elibrary.ru/MZYOZJ
4. Kolomoitsev Yu. Hardy-Littlewood and Ulyanov inequalities / Yu. Kolomoitsev, S. Tikhonov // Mem Amer. Soc. 271(1325) (2021), Arxiv: 1711.08163.
5. Domingues O. Embedding of smooth function spaces extrapolations, and related inequalities / O. Domingues, S. Tikhonov // ArXiv: 1909.12818v2 [math.FA] \ 22 \ Nov \ 2019 C. 1-71.
6. Potapov M. K. Utochnenie sootnosheniy mezhdu modulyami gladkosti / M. K. Potapov, B. V. Simonov // Vestn. Mosk. un-ta, ser. 1, Matematika. Mehanika. 2023. № 2. C. 11-23. DOI: https://doi.org/10.55959/MSU0579-9368-1-64-2-2; EDN: https://elibrary.ru/DFOTXO
