On the universal function for weighted spaces \(L^p_{\mu}[0,1], p\geq1\). (English) Zbl 1382.42016

Grigoryan, Martin; Grigoryan, Tigran; Sargsyan, Artsrun

Banach J. Math. Anal. 12, No. 1, 104-125 (2018).

Summary: In this article, we show that there exist a function \(g\in L^{1}[0,1]\) and a weight function \(0< \mu(x)\leq1\) so that \(g\) is universal for each class \(L^{p}_{\mu}[0,1]\), \(p\geq 1\), with respect to signs-subseries of its Fourier-Walsh series.

MSC:

42C10	Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
43A15	\(L^p\)-spaces and other function spaces on groups, semigroups, etc.

Keywords:

universal function; Fourier coefficients; Walsh system; weighted spaces; convergence in metric