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arXiv 2003.075632020-03-17math.FA

divergent Fourier series in function spaces near $L^1[0;1]$

Tengiz Kopaliani, Nino Samashvili, Shalva Zviadadze

DOI：: 10.1016/j.jmaa.2021.125558

英文摘要：

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.

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