Geodesic
Weakly Lacunary Orthogonal Systems and Properties of the Maximal Partial Sum Operator for Subsystems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 164-182

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For a finite orthogonal system of uniformly bounded functions, we establish the existence of sufficiently dense subsystems with the lacunarity property and a good norm estimate for the maximal partial sum operator. 
@article{TM_2020_311_a8,
     author = {B. S. Kashin and I. V. Limonova},
     title = {Weakly {Lacunary} {Orthogonal} {Systems} and {Properties} of the {Maximal} {Partial} {Sum} {Operator} for {Subsystems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {164--182},
     publisher = {mathdoc},
     volume = {311},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_311_a8/}
}
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B. S. Kashin; I. V. Limonova. Weakly Lacunary Orthogonal Systems and Properties of the Maximal Partial Sum Operator for Subsystems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 164-182. http://geodesic.mathdoc.fr/item/TM_2020_311_a8/