Hölder classes in the 𝐿^{𝑝} norm on a chord-arc curve in ℝ³

IF 0.7 4区数学 Q2 MATHEMATICS St Petersburg Mathematical Journal Pub Date : 2023-07-26 DOI:10.1090/spmj/1769

T. Alexeeva, N. Shirokov

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引用次数: 1

Abstract

The Hölder classes L p α ( L ) L_p^{\alpha } (L) in the L p ( L ) L_p(L) norm on a chord-arc curve L L in R 3 \mathbb {R}^3 are defined and direct and inverse approximation theorems are proved for functions from these classes by functions harmonic in a neighborhood of the curve. The approximation is estimated in the L p ( L ) L^p(L) norm, the direct theorem is proved for a certain subclass of L p α ( L ) L^\alpha _p(L) and the inverse theorem covers the entire Hölder class.

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在一个弦弧曲线上的𝐿^{𝑝}范数中的Hölder类

定义了弦弧曲线L L中的L p(L) L_p(L)范数L L在R 3 \mathbb {R}^3中的Hölder类L p α (L) L_p^{\alpha} (L)，并利用曲线邻域中的调和函数证明了这些类函数的正逼近定理和逆逼近定理。在L p(L) L^p(L)范数中估计了近似，证明了L p α (L) L^ α _p(L)的某个子类的正定理，逆定理涵盖了整个Hölder类。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

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