Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T14:32:27.048Z Has data issue: false hasContentIssue false
  • English
  • Français

Mean growth of the derivative of certain classes of analytic functions

Published online by Cambridge University Press:  24 October 2008

Daniel Girela
Daniel Girela
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we study the question of characterizing those positive Borel measures μ on the unit disc Δ for which the differentiation operator D defined by Df = f′ maps the Hardy space Hp continuously into the Bergman space Bp(dμ) of all functions f analytic in Δ which belong to Lp (Δ, dμ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 335 - 342
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Baernstein, A.. Analytic functions of bounded mean oscillation. In Aspects of Contemporary Complex Analysis (eds Brannan, D. and Clunie, J.), (Academic Press, 1980), pp. 3–36.Google Scholar
[2]Baernstein, A.. Review of [12]. Zentralblatt für Math. 661 (1989), no. 30040.Google Scholar
[3]Carleson, L.. An interpolation problem for bounded analytic functions. Amer. J. Math. 80 (1958), 921–930.CrossRefGoogle Scholar
[4]Carleson, L.. Interpolation by bounded analytic functions and the corona problem. Ann. of Math. 76 (1962), 547–559.CrossRefGoogle Scholar
[5]Duren, P. L.. Theory of HP Spaces (Academic Press, 1970).Google Scholar
[6]Eenigenburg, P. J.. The integral means of analytic functions. Quart. J. Math. Oxford Ser. (2) 32 (1981), 313–322.CrossRefGoogle Scholar
[7]Garnett, J. B.. Bounded Analytic Functions (Academic Press, 1981).Google Scholar
[8]Girela, D.. Mean growth of the derivative of an analytic function and bounded mean oscillation. Preprint.Google Scholar
[9]Littlewood, J. E. and Paley, R. E. A. C.. Theorems on Fourier series and power series (II). J. London Math. Soc. 42 (1931), 52–89.Google Scholar
[10]Mateljevic, M. and Pavlovic, M.. Multipliers of H P and BMOA. Pacific J. Math. 146 (1990), 71–84.CrossRefGoogle Scholar
[11]Rudin, W.. The radial variation of analytic functions. Duke Math. J. 22 (1955), 235–242.CrossRefGoogle Scholar
[12]Stroethoff, K.. Besov-type characterisations for the Bloch space. Bull. Austral. Math. Soc. 39 (1989), 405–420.CrossRefGoogle Scholar
[13]Zygmund, A.. Trigonometric Series (Cambridge University Press, 1959).Google Scholar