Relations between mixed moduli of smoothness, and embedding theorems for Nikol'skii classes

DOI10.1134/S0081543810020173zbMath1213.46032MaRDI QIDQ605975

B. V. Simonov, Mikhail K. Potapov, Sergey Yu. Tikhonov

Publication date: 15 November 2010

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuity and differentiation questions (26B05)

Related Items (10)

Refinement of the relations between mixed smoothness moduli in \(L_1\) and \(L_q\) metrics ⋮ Improvement of the Ul'yanov inequality for mixed moduli of smoothness for functions with lacunary Fourier coefficients ⋮ Refinement of relations between mixed moduli of smoothness in the metrics of \(L_p\) and \(L_\infty \) ⋮ Transformation of Fourier series by means of general monotone sequences ⋮ Relation between moduli of smoothness and partial sums of Fourier series and embedding theorems for Nikol'skii classes ⋮ Mixed modulus of continuity in the Lebesgue spaces with Muckenhouptweights and their properties ⋮ Mixed modulus of smoothness with Muckenhoupt weights and approximation by angle ⋮ Fractional order mixed difference operator and its applications in angular approximation ⋮ Inequalities refining relations between mixed moduli of smoothness in \(L_1\) and \(L_q\) metrics ⋮ Properties of mixed moduli of smoothness of functions with lacunary Fourier coefficients

Cites Work

• Unnamed Item
• Sharp Ul'yanov-type inequalities using fractional smoothness
• On the interrelation of the generalized Besov-Nikols'kiǐ and Weyl-Nikols'kiǐ classes of functions
• Relations between moduli of smoothness in different metrics

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