On the Structure of Functions, Universal for Weighted Spaces \(L_\mu ^p\left[ {0,1} \right],p > 1\)
- 作者: Sargsyan A.1
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隶属关系:
- Russian-Armenian University
- 期: 卷 54, 编号 3 (2019)
- 页面: 163-175
- 栏目: Real and Complex Analysis
- URL: https://journals.rcsi.science/1068-3623/article/view/228330
- DOI: https://doi.org/10.3103/S1068362319030051
- ID: 228330
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详细
The paper is devoted to the questions relating the structure of universal functions for weighted spaces \(L_\mu ^p\left[{0,\;1} \right],\;p > 1\). We prove existence of a measurable set E ⊂ [0, 1] with measure arbitrarily close to 1, and a weight function 0 < µ(x) ≤ 1, equal to 1 on E, such that by suitable continuation of an arbitrary function f ∈ L1(E) on [0, 1] \ E, a function \(\widetilde{f}\; \in \;{L^1}\left[{0,\;1} \right]\) can be obtained, which is universal for each class \(L_\mu ^p\left[{0,\;1} \right],\;p > 1\), in the sense of subsequences of signs of its Fourier-Walsh coefficients.