Geodesic
Generalized Markov--Stieltjes operator on Hardy and Lebesgue spaces
Trudy Instituta matematiki, Tome 25 (2017) no. 1, pp. 39-50.

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Generalized Markov–Stieltjes operator $S_\alpha$ is introduced, inverse formulas and operational properties for corresponding integral transform obtained, boundedness, nuclearity or compactness of operator $S_\alpha$ on Hardy and Lebesgue spaces for various values of complex parameter $\alpha$ proved, its trace is calculated, and estimates for its norm are given. 
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I. S. Kovalyova; A. R. Mirotin. Generalized Markov--Stieltjes operator on Hardy and Lebesgue spaces. Trudy Instituta matematiki, Tome 25 (2017) no. 1, pp. 39-50. http://geodesic.mathdoc.fr/item/TIMB_2017_25_1_a3/

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