论文标题
$ l^1 [0; 1] $附近的功能空间中的傅立叶系列序列发散系列
divergent Fourier series in function spaces near $L^1[0;1]$
论文作者
论文摘要
在本文中，我们概括了Bochkariev的定理，该定理指出，对于任何均匀界限的正常系统$φ$，存在Lebesgue Entighable ablectable函数，以使其相对于系统$φ$差异的傅立叶序列在一组积极度量上差异。我们表征了变量指数lebesgue spaces的类别$ l^{p（\ cdot）} [0; 1] $，$ 1 <p（x）<\ infty $ a.e.在[0; 1]上，因此上述Bochkarev的定理是有效的。
In this paper we generalize Bochkariev's theorem, which states that for any uniformly bounded orthonormal system $Φ$, there exists a Lebesgue integrable function such that the Fourier series of it with respect to system $Φ$ diverge on the set of positive measure. We characterize the class of variable exponent Lebesgue spaces $L^{p(\cdot)}[0;1]$, $1<p(x)<\infty$ a.e. on [0;1], such that above mentioned Bochkarev's theorem is valid.
