Abstract
After some preliminaries, which identify the conjugate operator with the Hilbert transform, we prove the famous Marcel Riesz theorem and some of its variants. Then we discuss the more recent, but also most basic, theorem that the conjugate function and the nontangential maximal function belong to the same Lp classes.
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© 2007 Springer
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Garnett, J.B. (2007). Conjugate Functions. In: Bounded Analytic Functions. Graduate Texts in Mathematics, vol 236. Springer, New York, NY. https://doi.org/10.1007/0-387-49763-3_3
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DOI: https://doi.org/10.1007/0-387-49763-3_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-33621-3
Online ISBN: 978-0-387-49763-1
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