Book Review
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MathSciNet review:
4076539
Full text of review:
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Book Information:
Author:
Nikolaï Nikolski
Title:
Hardy spaces
Additional book information:
Cambridge Studies in Advanced Mathematics, Vol. 179,
Cambridge University Press,
Cambridge,
2019,
xviii+227 pp.,
ISBN 978-1-107-18454-1,
US$64.99
Translated from the 2012 French edition
Peter Duren and Alexander Schuster, Bergman spaces, Mathematical Surveys and Monographs, vol. 100, American Mathematical Society, Providence, RI, 2004. MR 2033762, DOI 10.1090/surv/100
Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
Omar El-Fallah, Karim Kellay, Javad Mashreghi, and Thomas Ransford, A primer on the Dirichlet space, Cambridge Tracts in Mathematics, vol. 203, Cambridge University Press, Cambridge, 2014. MR 3185375
Stephan Ramon Garcia, Javad Mashreghi, and William T. Ross, Introduction to model spaces and their operators, Cambridge Studies in Advanced Mathematics, vol. 148, Cambridge University Press, Cambridge, 2016. MR 3526203, DOI 10.1017/CBO9781316258231
John B. Garnett, Bounded analytic functions, 1st ed., Graduate Texts in Mathematics, vol. 236, Springer, New York, 2007. MR 2261424
Haakan Hedenmalm, Boris Korenblum, and Kehe Zhu, Theory of Bergman spaces, Graduate Texts in Mathematics, vol. 199, Springer-Verlag, New York, 2000. MR 1758653, DOI 10.1007/978-1-4612-0497-8
Kenneth Hoffman, Banach spaces of analytic functions, Dover Publications, Inc., New York, 1988. Reprint of the 1962 original. MR 1102893
N. K. Nikol′skiĭ, Treatise on the shift operator, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 273, Springer-Verlag, Berlin, 1986. Spectral function theory; With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller; Translated from the Russian by Jaak Peetre. MR 827223, DOI 10.1007/978-3-642-70151-1
Nikolai K. Nikolski, Operators, functions, and systems: an easy reading. Vol. 1, Mathematical Surveys and Monographs, vol. 92, American Mathematical Society, Providence, RI, 2002. Hardy, Hankel, and Toeplitz; Translated from the French by Andreas Hartmann. MR 1864396
Nikolai K. Nikolski, Operators, functions, and systems: an easy reading. Vol. 2, Mathematical Surveys and Monographs, vol. 93, American Mathematical Society, Providence, RI, 2002. Model operators and systems; Translated from the French by Andreas Hartmann and revised by the author. MR 1892647
Béla Sz.-Nagy, Ciprian Foias, Hari Bercovici, and László Kérchy, Harmonic analysis of operators on Hilbert space, Revised and enlarged edition, Universitext, Springer, New York, 2010. MR 2760647, DOI 10.1007/978-1-4419-6094-8
References
- Peter Duren and Alexander Schuster, Bergman spaces, Mathematical Surveys and Monographs, vol. 100, American Mathematical Society, Providence, RI, 2004. MR 2033762, DOI 10.1090/surv/100
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- Omar El-Fallah, Karim Kellay, Javad Mashreghi, and Thomas Ransford, A primer on the Dirichlet space, Cambridge Tracts in Mathematics, vol. 203, Cambridge University Press, Cambridge, 2014. MR 3185375
- Stephan Ramon Garcia, Javad Mashreghi, and William T. Ross, Introduction to model spaces and their operators, Cambridge Studies in Advanced Mathematics, vol. 148, Cambridge University Press, Cambridge, 2016. MR 3526203, DOI 10.1017/CBO9781316258231
- John B. Garnett, Bounded analytic functions, 1st ed., Graduate Texts in Mathematics, vol. 236, Springer, New York, 2007. MR 2261424
- Haakan Hedenmalm, Boris Korenblum, and Kehe Zhu, Theory of Bergman spaces, Graduate Texts in Mathematics, vol. 199, Springer-Verlag, New York, 2000. MR 1758653, DOI 10.1007/978-1-4612-0497-8
- Kenneth Hoffman, Banach spaces of analytic functions, Dover Publications, Inc., New York, 1988. Reprint of the 1962 original. MR 1102893
- N. K. Nikolski, Treatise on the shift operator: Spectral function theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 273, Springer-Verlag, Berlin, 1986. With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller; Translated from the Russian by Jaak Peetre. MR 827223, DOI 10.1007/978-3-642-70151-1
- Nikolai K. Nikolski, Operators, functions, and systems: an easy reading. Vol. 1: Hardy, Hankel, and Toeplitz, Mathematical Surveys and Monographs, vol. 92, American Mathematical Society, Providence, RI, 2002. Translated from the French by Andreas Hartmann. MR 1864396
- Nikolai K. Nikolski, Operators, functions, and systems: an easy reading. Vol. 2: Model operators and systems, Mathematical Surveys and Monographs, vol. 93, American Mathematical Society, Providence, RI, 2002. Translated from the French by Andreas Hartmann and revised by the author. MR 1892647
- Béla Sz.-Nagy, Ciprian Foias, Hari Bercovici, and László Kérchy, Harmonic analysis of operators on Hilbert space, Revised and enlarged edition, Universitext, Springer, New York, 2010. MR 2760647, DOI 10.1007/978-1-4419-6094-8
Review Information:
Reviewer:
William T. Ross
Affiliation:
Department of Mathematics and Computer Science, University of Richmond, Richmond, Virginia 23173
Email:
wross@richmond.edu
Journal:
Bull. Amer. Math. Soc.
57 (2020), 347-352
DOI:
https://doi.org/10.1090/bull/1686
Published electronically:
November 19, 2019
Review copyright:
© Copyright 2019
American Mathematical Society
