Skip to main content
×
×
Home

CLASSICAL PROPERTIES OF COMPOSITION OPERATORS ON HARDY–ORLICZ SPACES ON PLANAR DOMAINS

  • MICHAŁ RZECZKOWSKI (a1)
Abstract

In this paper we study composition operators on Hardy–Orlicz spaces on multiply connected domains whose boundaries consist of finitely many disjoint analytic Jordan curves. We obtain a characterization of order-bounded composition operators. We also investigate weak compactness and the Dunford–Pettis property of these operators.

Copyright
Footnotes
Hide All

This research was supported by National Science Centre research grant 2015/19/N/ST1/00845.

Footnotes
References
Hide All
[1] Cowen, C. and MacCluer, B., Composition Operators on Spaces of Analytic Functions (CRC Press, Boca Raton, FL, 1995).
[2] Fisher, S. D., Function Theory on Planar Domains (Wiley, New York, 1983).
[3] Fisher, S. D. and Shapiro, J. E., ‘The essential norm of composition operators on a planar domain’, Illinois J. Math. 43 (1999), 113130.
[4] Forelli, F., ‘The isometries of H p ’, Canad. J. Math. 16 (1964), 721728.
[5] Garnett, J. B. and Marshall, D. E., Harmonic Measure (Cambridge University Press, New York, 2005).
[6] Krasnosielskii, M. A. and Rutycki, J. B., Convex Functions and Orlicz Spaces (Noordhoff, Groningen, 1961).
[7] Lefèvre, P., Li, D., Queffélec, H. and Rodríguez-Piazza, L., ‘A criterion of weak compactness for operators on subspaces of Orlicz spaces’, J. Funct. Spaces Appl. 6(3) (2008), 277292.
[8] Lefèvre, P., Li, D., Queffélec, H. and Rodríguez-Piazza, L., ‘Some examples of compact composition operators on H 2 ’, J. Funct. Anal. 255(11) (2008), 30983124.
[9] Lefèvre, P., Li, D., Queffélec, H. and Rodríguez-Piazza, L., ‘Compact composition operators on H 2 and Hardy–Orlicz spaces’, J. Math. Anal. Appl. 354(1) (2009), 360371.
[10] Lefèvre, P., Li, D., Queffélec, H. and Rodríguez-Piazza, L., ‘Composition operators on Hardy–Orlicz spaces’, Mem. Amer. Math. Soc. 207(974) (2010), 174.
[11] Lefèvre, P., Li, D., Quefféleci, H. and Rodríguez-Piazza, L., ‘Nevanlinna counting function and Carleson function of analytic maps’, Math. Ann. 351 (2011), 305326.
[12] MacCluer, B. D., ‘Compact composition operators on H p (B N )’, Michigan Math. J. 32 (1985), 237248.
[13] Mastyło, M. and Mleczko, P., ‘Solid hulls of quasi-Banach spaces of analytic functions and interpolation’, Nonlinear Anal. 73(1) (2010), 8498.
[14] Rao, M. M. and Ren, Z. D., Theory of Orlicz Spaces, Pure and Applied Mathematics, 146 (Marcel Dekker, New York, 1991).
[15] Rudin, W., ‘Analytic functions of class H p ’, Trans. Amer. Math. Soc. 78 (1955), 4666.
[16] Rzeczkowski, M., ‘Composition operators on Hardy–Orlicz spaces on planar domains’, Ann. Acad. Sci. Fenn. Math. 42 (2017), 593609.
[17] Sarason, D., ‘The H p spaces of an annulus’, Mem. Amer. Math. Soc. 56 (1965), 178.
[18] Shapiro, J. H., ‘The essential norm of a composition operator’, Ann. of Math. (2) 125 (1987), 375404.
[19] Shapiro, J. H., Composition Operators and Classical Function Theory (Springer, New York, 1991).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed