Abstract
It is shown that there exist such a function \(g\in L^1[0,1]\) and a weight function \(0<\mu (x)\le 1\) that g is universal for the weighted space \(L^1_\mu [0,1]\) with respect to signs of its Fourier–Walsh coefficients.
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Sargsyan, A., Grigoryan, M. Universal function for a weighted space \(L^1_{\mu }[0,1]\) . Positivity 21, 1457–1482 (2017). https://doi.org/10.1007/s11117-017-0479-8
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DOI: https://doi.org/10.1007/s11117-017-0479-8