Estimates for the Best M-Term Approximations of Functions of Class Wq,τ,θa,b·,r¯ in the Lorentz Space
Myrzagaliyeva A. Akishev G.
June 2025Springer
Journal of Mathematical Sciences (United States)
2025#291Issue 2282 - 301 pp.
We consider the Lorentz space Lq,τ(Tm) of periodic functions of m variables and the class Wq,τ,θa,b·,r¯ with 1 < q, τ < ∞, a > 0, 1 < θ ⩽ ∞, where b(t) is a weakly oscillating function on [1, ∞). We find a sufficient condition on a function f ∈ Lq,τ1(Tm) to belong to the space Lq,τ2(Tm) with 1 < q < p < ∞, 1 < τ1 < τ2 < ∞ and the embedding Wq,τ1,θa,b·,r¯ ⊂ Lq,τ2(Tm). We obtain upper bounds for the best M-term trigonometric approximations of functions of class Wq,τ1,θa,b·,r¯ in the Lq,τ2(Tm)-norm in the case 1 < q < 2 < p < ∞ under some conditions on a, τ1, τ2. For some values of a, τ1, τ2, the accuracy of the upper bound is established.
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Astana IT University, 55/11, Mangilik El Av., Astana, 020000, Kazakhstan
Kazakhstan Branch of Lomonosov Moscow State University, 11, Kazhymukan Munaitpasov St., Astana, 020000, Kazakhstan
Astana IT University
Kazakhstan Branch of Lomonosov Moscow State University
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