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arXiv · 1611.06584

The Markov-Stieltjes transform as an operator

A. R. Mirotin·I. S. Kovalyova
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Abstract

We prove that the Markov-Stieltjes transform is a bounded non compact Hankel operator on Hardy space $H^p$ with Hilbert matrix with respect to the standard Schauder basis of $H^p$ and a bounded non compact operator on Lebesgue space $L^p[0,1]$ for $p\in(1,\infty)$ and obtain estimates for its norm in this spaces. It is shown that the Markov-Stieltjes transform on $L^2(0,1)$ is unitary equivalent to the Markov-Stieltjes transform on $H^2$. Inverse formulas and operational properties for this transform are obtained.

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A. R. Mirotin, I. S. Kovalyova. 2016-11-20. The Markov-Stieltjes transform as an operator. https://arxiv.org/abs/1611.06584

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