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- Title
Kolmogorov-type inequalities for norms of Riesz derivatives of functions of several variables with Laplacian bounded in L and related problems.
- Authors
Babenko, V.; Parfinovich, N.; Pichugov, S.
- Abstract
Let L(ℝ) be the space of functions f ∈ L(ℝ) such that Δ f ∈ L(ℝ). We obtain new sharp Kolmogorov-type inequalities for the L-norms of the Riesz derivatives D f of the functions f ∈ L(ℝ) and solve the Stechkin problem of approximating an unbounded operator D by bounded operators on the class f ∈ L(ℝ) such that |Δ f| ≤ 1, and also the problem of the best recovery of the operator D from elements of this class given with error δ.
- Subjects
KOLMOGOROV complexity; RIESZ spaces; MATHEMATICAL inequalities; LAPLACIAN operator; FUNCTIONS of bounded variation
- Publication
Mathematical Notes, 2014, Vol 95, Issue 1/2, p3
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434614010015