On estimates of n-term approximations of functions in Lorentz space
ОБ ОЦЕНКАХ n-ЧЛЕННЫХ ПРИБЛИЖЕНИЙ ФУНКЦИЙ В ПРОСТРАНСТВЕ ЛОРЕНЦА
Akishev G.
26 November 2025Krasovskii Institute of Mathematics and Mechanics
Trudy Instituta Matematiki i Mekhaniki UrO RAN
2025#31Issue 410 - 25 pp.
The article considers the Lorentz space Lq,t (Tm) of periodic functions of m variables and the class (formula presented) for 1 < q, _ < ∞, a > 0, b(t) is a slowly varying function on [1, ∞). (formula presented) the class of all functions f ∈ Lq,t,_ (Tm) for which (formula presentd) the partial sum over the step hyperbolic cross of the Fourier series in the norm of Lq,t_ (Tm) converges at rate 2−nab(2n) as n → ∞. The main result is the exact order of the best n-term trigonometric approximations of functions from the class (formla presented) in the norm of the space Lp,T2 (Tm) in the case 1 < q < p 6 2, for some relations between the parameters a, T1, T2. The result is proved by a constructive method.
best n-term approximation , constructive method , Lorentz space , trigonometric system
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Lomonosov Moscow University, Kazakhstan Branch, Astana, 100001, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Lomonosov Moscow University
Institute of Mathematics and Mathematical Modeling
10 лет помогаем публиковать статьи Международный издатель
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