IMBEDDING THEOREMS AND RELATIONS BETWEEN BEST APPROXIMATIONS (MODULI OF CONTINUITY) IN DIFFERENT METRICS

DOI10.1070/SM1970v010n01ABEH001589zbMath0215.17702OpenAlexW2031561208MaRDI QIDQ5617949

P. L. Ul'yanov

Publication date: 1970

Published in: Mathematics of the USSR-Sbornik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm1970v010n01abeh001589

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) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Trigonometric polynomials, inequalities, extremal problems (42A05)

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Refinement of the relations between mixed smoothness moduli in \(L_1\) and \(L_q\) metrics ⋮ Interrelations between full moduli of smoothness in the metrics of \(L_1\) and \(L_\infty\) ⋮ Kolyada inequality for partial moduli of smoothness of functions with lacunary Fourier coefficients ⋮ Fourier-Price coefficients of class GM and best approximations of functions in the Lorentz space \(L_{p\theta}[0, 1)\), \(1<p<+\infty\), \(1<\theta<+\infty\) ⋮ Interrelations between mixed moduli of smoothness in metrics of \(L_p\) and \(L_\infty\) ⋮ Sharp Ul'yanov-type inequalities using fractional smoothness ⋮ Refinement of relations between mixed moduli of smoothness in the metrics of \(L_p\) and \(L_\infty \) ⋮ The direct theorem of the theory of approximation of periodic functions with monotone Fourier coefficients in different metrics ⋮ A characterization of Besov classes in terms of a new modulus of continuity ⋮ ORDER EQUALITIES IN DIFFERENT METRICS FOR MODULI OF SMOOTHNESS OF VARIOUS ORDERS ⋮ Ulyanov-type embedding theorems for functions on zero-dimensional locally compact groups ⋮ Connection between moduli of smoothness in the metrics of \(L_p\) and \(C\) ⋮ Kernels and best approximations related to the system of ultraspherical polynomials ⋮ Estimates of mixed moduli of smoothness in metrics of \(L_q\) through mixed moduli of smoothness in metrics of \(L_1\) ⋮ Besov classes on finite and infinite dimensional spaces

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