Refinement of relations between mixed moduli of smoothness in the metrics of \(L_p\) and \(L_\infty \)

DOI10.1134/S0001434621090054zbMath1489.46038OpenAlexW3210837159MaRDI QIDQ2666603

B. V. Simonov, Mikhail K. Potapov

Publication date: 23 November 2021

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434621090054

zbMATH Keywords

metricinequalitymixed modulus of smoothness of fractional order

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Fractional derivatives and integrals (26A33) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Cites Work

• Relations between mixed moduli of smoothness, and embedding theorems for Nikol'skii classes
• Sharp Ul'yanov-type inequalities using fractional smoothness
• On relations between moduli of continuity in different metrics
• Trigonometric series with general monotone coefficients
• Trigonometric series of Nikol'skii classes
• Weak type inequalities for moduli of smoothness: The case of limit value parameters
• Interrelations between mixed moduli of smoothness in metrics of \(L_p\) and \(L_\infty\)
• Relations between moduli of smoothness in different metrics
• Ulyanov-type inequalities and generalized Liouville derivatives
• Mixed Moduli of Smoothness in $L_p$, $1<p<\infty$
• THE IMBEDDING OF CERTAIN FUNCTION CLASSESH_p^ω
• IMBEDDING THEOREMS AND RELATIONS BETWEEN BEST APPROXIMATIONS (MODULI OF CONTINUITY) IN DIFFERENT METRICS
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