Geodesic
On summability of the Fourier coefficients in bounded orthonormal systems for functions from some Lorentz type spaces
Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 76-85

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We denote by $\Lambda_\beta(\lambda),$ $\beta>0,$ the Lorentz space equipped with the (quasi) norm $$ \|f\|_{\Lambda_\beta(\lambda)}:=\left(\int_0^1\left(f^*(t)t\lambda\left(\frac1t\right)\right)^\beta\frac{dt}{t}\right)^{\frac1\beta} $$ for a function $f$ on [0,1] and with $\lambda$ positive and equipped with some additional growth properties. Some estimates of this quantity and some corresponding sums of Fourier coefficients are proved for the case with a general orthonormal bounded system. 
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     author = {A. N. Kopezhanova and L.-E. Persson},
     title = {On summability of the {Fourier} coefficients in bounded orthonormal systems for functions from some {Lorentz} type spaces},
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A. N. Kopezhanova; L.-E. Persson. On summability of the Fourier coefficients in bounded orthonormal systems for functions from some Lorentz type spaces. Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 76-85. http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a4/