On estimates of M-term approximations of the Sobolev class in the Lorentz space
Лоренц кеңiстiгiндегi Соболев класының M-мүшелiк жуықтауларын бағалау туралы
Об оценках M-членных приближений класса Соболева в пространстве Лоренца
Akishev G. Myrzagaliyeva A.K.
2024E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2024#114Issue 24 - 21 pp.
In the paper spaces of periodic functions of several variables were considered, namely the Lorentz space L2,τ(Tm), the class of functions with bounded mixed fractional derivative W2r,τ, 1 ≤ τ < ∞, and the order of the best M-term approximation of a function f ∈ Lp,τ(Tm) by trigonometric polynomials was studied. The article consists of an introduction, a main part, and a conclusion. In the introduction, basic concepts, definitions and necessary statements for the proof of the main results were considered. One can be found information about previous results on the mentioned topic. In the main part, exact-order estimates are established for the best M-term approximations of functions of the Sobolev class W2r,τ1 in the norm of the space Lp,τ2(Tm) for various relations between the parameters p,τ1,τ2.
Lorentz space , M-term approximation , mixed derivative , Sobolev class , trigonometric polynomial
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