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Классы Гёльдера в L^p-норме на chord-arc кривой в R^3

Алгебра и анализ. 2022. Т. 34. № 4. С. 1–21.
Alexeeva T., Shirokov N. A.

We define Holder classes L^p_α(L) in the L^p(L) norm on a chord-arc curve L in R^3 and prove direct and inverse approximation theorems for functions from these classes by functions harmonic in a neighborhood of the curve. The approximation is estimated in the L^p(L) norm, and the smaller the neighborhood, the more accurate the approximation.

Research target: Mathematics
Language: Russian
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Keywords: harmonic functionsгармонические функцииHolder classesconstructive description chord-arc curvesконструктивное описаниегёльдеровские классысhord-arc кривые
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