Composition operators and the Hilbert matrix

E. Diamantopoulos; Aristomenis Siskakis

Studia Mathematica (2000)

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

Abstract

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

How to cite

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Diamantopoulos, 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

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  1. [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. 
  2. [DU] P. L. Duren, Theory of H p Spaces, Academic Press, New York, 1970. 
  3. [CM] C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1995. Zbl0873.47017
  4. [HLP] G. Hardy, J. E. Littlewood and G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, 1988. Zbl0634.26008
  5. [PA] J. R. Partington, An Introduction to Hankel Operators, London Math. Soc. Student Texts 13, Cambridge Univ. Press, 1988. 
  6. [SH] J. H. Shapiro, Composition Operators and Classical Function Theory, Springer, New York, 1993. 
  7. [WW] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, 1978. 

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