Potapov, M. K.; Simonov, B. V. Improvement of relations between moduli of smoothness. (English. Russian original) Zbl 1518.26008 Mosc. Univ. Math. Bull. 78, No. 2, 67-82 (2023); translation from Vestn. Mosk. Univ., Ser. I 78, No. 2, 11-23 (2023). Reviewer: Peter Massopust (München) MSC: 26A33 26A15 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Mosc. Univ. Math. Bull. 78, No. 2, 67--82 (2023; Zbl 1518.26008); translation from Vestn. Mosk. Univ., Ser. I 78, No. 2, 11--23 (2023) Full Text: DOI
Potapov, M. K.; Simonov, B. V. Inequalities refining relations between mixed moduli of smoothness in \(L_1\) and \(L_q\) metrics. (English. Russian original) Zbl 1512.46022 Russ. Math. 66, No. 2, 36-52 (2022); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2022, No. 2, 43-61 (2022). MSC: 46E30 41A17 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Russ. Math. 66, No. 2, 36--52 (2022; Zbl 1512.46022); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2022, No. 2, 43--61 (2022) Full Text: DOI
Potapov, M. K.; Simonov, B. V. Kolyada inequality between mixed moduli of smoothness in metrics \(L_p\) and \(L_{\infty} \). (English. Russian original) Zbl 1504.42002 Mosc. Univ. Math. Bull. 77, No. 4, 161-175 (2022); translation from Vestn. Mosk. Univ., Ser. I 77, No. 4, 3-15 (2022). MSC: 42A10 42A05 46E35 41A50 26A33 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Mosc. Univ. Math. Bull. 77, No. 4, 161--175 (2022; Zbl 1504.42002); translation from Vestn. Mosk. Univ., Ser. I 77, No. 4, 3--15 (2022) Full Text: DOI
Potapov, M. K.; Simonov, B. V. Refinement of relations between mixed moduli of smoothness in the metrics of \(L_p\) and \(L_\infty \). (English. Russian original) Zbl 1489.46038 Math. Notes 110, No. 3, 347-362 (2021); translation from Mat. Zametki 110, No. 3, 368-385 (2021). MSC: 46E30 41A17 26A33 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Math. Notes 110, No. 3, 347--362 (2021; Zbl 1489.46038); translation from Mat. Zametki 110, No. 3, 368--385 (2021) Full Text: DOI
Potapov, M. K.; Simonov, B. V. Refinement of the relations between mixed smoothness moduli in \(L_1\) and \(L_q\) metrics. (English. Russian original) Zbl 1481.41008 Sib. Math. J. 62, No. 4, 661-677 (2021); translation from Sib. Mat. Zh. 62, No. 4, 812-829 (2021). Reviewer: Zoltán Finta (Cluj-Napoca) MSC: 41A25 26A15 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Sib. Math. J. 62, No. 4, 661--677 (2021; Zbl 1481.41008); translation from Sib. Mat. Zh. 62, No. 4, 812--829 (2021) Full Text: DOI
Potapov, Mikhaĭl Konstantinovich; Simonov, Boris Vital’evich Estimates of partial moduli of smoothness in metrics of \(L_{p_1 \infty }\) and \(L_{ \infty p_2}\) through partial moduli of smoothness in metrics of \(L_{p_1p_2}\). (English. Russian original) Zbl 1446.26003 Mosc. Univ. Math. Bull. 75, No. 1, 1-15 (2020); translation from Vestn. Mosk. Univ., Ser. I 75, No. 1, 3-17 (2020). Reviewer: Włodzimierz Łenski (Poznań) MSC: 26A15 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Mosc. Univ. Math. Bull. 75, No. 1, 1--15 (2020; Zbl 1446.26003); translation from Vestn. Mosk. Univ., Ser. I 75, No. 1, 3--17 (2020) Full Text: DOI
Potapov, M. K.; Simonov, B. V. Strengthened Ul’yanov’s inequalities for partial moduli of smoothness for functions from spaces with various metrics. (English. Russian original) Zbl 1431.41006 Mosc. Univ. Math. Bull. 74, No. 3, 108-120 (2019); translation from Vestn. Mosk. Univ., Ser. I 74, No. 3, 26-38 (2019). MSC: 41A17 26B05 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Mosc. Univ. Math. Bull. 74, No. 3, 108--120 (2019; Zbl 1431.41006); translation from Vestn. Mosk. Univ., Ser. I 74, No. 3, 26--38 (2019) Full Text: DOI
Potapov, M. K.; Simonov, B. V. Nikolskii inequalities for trigonometric polynomials in different metrics. (English. Russian original) Zbl 1477.41005 Russ. Math. 63, No. 1, 42-54 (2019); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2019, No. 1, 49-62 (2019). MSC: 41A17 42A10 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Russ. Math. 63, No. 1, 42--54 (2019; Zbl 1477.41005); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2019, No. 1, 49--62 (2019) Full Text: DOI
Potapov, M. K.; Simonov, B. V. Strengthened Ul’yanov’s inequality for complete moduli of smoothness of functions from spaces with mixed metrics. (English. Russian original) Zbl 1423.41014 Mosc. Univ. Math. Bull. 73, No. 6, 217-228 (2018); translation from Vestn. Mosk. Univ., Ser. I 73, No. 6, 8-20 (2018). MSC: 41A17 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Mosc. Univ. Math. Bull. 73, No. 6, 217--228 (2018; Zbl 1423.41014); translation from Vestn. Mosk. Univ., Ser. I 73, No. 6, 8--20 (2018) Full Text: DOI
Potapov, M. K.; Simonov, B. V. Estimates of mixed moduli of smoothness in metrics of \(L_q\) through mixed moduli of smoothness in metrics of \(L_1\). (English. Russian original) Zbl 1406.46027 Mosc. Univ. Math. Bull. 73, No. 2, 50-63 (2018); translation from Vestn. Mosk. Univ., Ser. I 73, No. 2, 12-26 (2018). MSC: 46E35 41A17 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Mosc. Univ. Math. Bull. 73, No. 2, 50--63 (2018; Zbl 1406.46027); translation from Vestn. Mosk. Univ., Ser. I 73, No. 2, 12--26 (2018) Full Text: DOI
Berisha, Nimete Sh.; Berisha, Faton M.; Potapov, Mikhail K.; Dema, Marjan On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness. (English) Zbl 1470.42005 Abstr. Appl. Anal. 2017, Article ID 9323181, 11 p. (2017). MSC: 42A10 PDFBibTeX XMLCite \textit{N. Sh. Berisha} et al., Abstr. Appl. Anal. 2017, Article ID 9323181, 11 p. (2017; Zbl 1470.42005) Full Text: DOI arXiv
Potapov, M. K.; Simonov, B. V. Interrelations between mixed moduli of smoothness in metrics of \(L_p\) and \(L_\infty\). (English. Russian original) Zbl 1384.46029 Mosc. Univ. Math. Bull. 72, No. 3, 107-120 (2017); translation from Vestn. Mosk. Univ., Ser. I 72, No. 3, 21-35 (2017). MSC: 46E35 41A17 42B05 26A33 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Mosc. Univ. Math. Bull. 72, No. 3, 107--120 (2017; Zbl 1384.46029); translation from Vestn. Mosk. Univ., Ser. I 72, No. 3, 21--35 (2017) Full Text: DOI
Potapov, M. K.; Simonov, B. V. Properties of the mixed modulus of smoothness of positive order in a mixed metric. (English. Russian original) Zbl 1328.46026 Mosc. Univ. Math. Bull. 69, No. 6, 258-266 (2014); translation from Vestn. Mosk. Univ., Ser. I 69, No. 6, 31-40 (2014). MSC: 46E30 26B05 41A17 PDFBibTeX XMLCite \textit{M. K. Potapov} and \textit{B. V. Simonov}, Mosc. Univ. Math. Bull. 69, No. 6, 258--266 (2014; Zbl 1328.46026); translation from Vestn. Mosk. Univ., Ser. I 69, No. 6, 31--40 (2014) Full Text: DOI