Geodesic
On Lebesgue Functions of Uniformly Bounded Orthonormal Systems
Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 181-193

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A complement to A. M. Olevskii's fundamental inequality on the logarithmic growth of Lebesgue functions of an arbitrary uniformly bounded orthonormal system on a set of positive measure is made. Namely, the index where the Lebesgue functions have growth slightly weaker than logarithmic can be chosen independently of the variable. The theorem proved in this paper improves a result established earlier by the author. 
@article{MZM_2001_69_2_a2,
     author = {R. D. Getsadze},
     title = {On {Lebesgue} {Functions} of {Uniformly} {Bounded} {Orthonormal} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {181--193},
     publisher = {mathdoc},
     volume = {69},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a2/}
}
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R. D. Getsadze. On Lebesgue Functions of Uniformly Bounded Orthonormal Systems. Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 181-193. http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a2/