# Composition operators and the Hilbert matrix

E. Diamantopoulos; Aristomenis Siskakis

Studia Mathematica (2000)

- Volume: 140, Issue: 2, page 191-198
- ISSN: 0039-3223

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topDiamantopoulos, E., and Siskakis, Aristomenis. "Composition operators and the Hilbert matrix." Studia Mathematica 140.2 (2000): 191-198. <http://eudml.org/doc/216762>.

@article{Diamantopoulos2000,

abstract = {The Hilbert matrix acts on Hardy spaces by multiplication with Taylor coefficients. We find an upper bound for the norm of the induced operator.},

author = {Diamantopoulos, E., Siskakis, Aristomenis},

journal = {Studia Mathematica},

keywords = {Hilbert inequality; Hilbert matrix; Hardy spaces; Hankel operator},

language = {eng},

number = {2},

pages = {191-198},

title = {Composition operators and the Hilbert matrix},

url = {http://eudml.org/doc/216762},

volume = {140},

year = {2000},

}

TY - JOUR

AU - Diamantopoulos, E.

AU - Siskakis, Aristomenis

TI - Composition operators and the Hilbert matrix

JO - Studia Mathematica

PY - 2000

VL - 140

IS - 2

SP - 191

EP - 198

AB - The Hilbert matrix acts on Hardy spaces by multiplication with Taylor coefficients. We find an upper bound for the norm of the induced operator.

LA - eng

KW - Hilbert inequality; Hilbert matrix; Hardy spaces; Hankel operator

UR - http://eudml.org/doc/216762

ER -

## References

top- [CS] J. A. Cima and D. A. Stegenga, Hankel operators on ${H}^{p}$, in: Analysis in Urbana, Vol. I, London Math. Soc. Lecture Note Ser. 137, Cambridge Univ. Press, 1989, 133-150.
- [DU] P. L. Duren, Theory of ${H}^{p}$ Spaces, Academic Press, New York, 1970.
- [CM] C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1995. Zbl0873.47017
- [HLP] G. Hardy, J. E. Littlewood and G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, 1988. Zbl0634.26008
- [PA] J. R. Partington, An Introduction to Hankel Operators, London Math. Soc. Student Texts 13, Cambridge Univ. Press, 1988.
- [SH] J. H. Shapiro, Composition Operators and Classical Function Theory, Springer, New York, 1993.
- [WW] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, 1978.

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