Rocky Mountain Journal of Mathematics

Some Results on Mean Lipschitz Spaces of Analytic Functions

Daniel Girela and Cristóbal González

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 30, Number 3 (2000), 901-922.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30D55
Secondary: 30D50


Girela, Daniel; González, Cristóbal. Some Results on Mean Lipschitz Spaces of Analytic Functions. Rocky Mountain J. Math. 30 (2000), no. 3, 901--922. doi:10.1216/rmjm/1021477251.

Export citation


  • J.M. Anderson, J. Clunie and Ch. Pommerenke, On Bloch functions and normal functions, J. Reine Angew. Math. 270 (1974), 12-37.
  • R. Aulaskari, D.A. Stegenga and J. Xiao, Some subclasses of BMOA and their characterization in terms of Carleson measures, Rocky Mountain J. Math. 26 (1996), 485-506.
  • A. Baernstein, Analytic functions of bounded mean oscillation, in Aspects of contemporary complex analysis (D. Brannan and J. Clunie, eds.), Academic Press, New York, 1980, 3-36.
  • A. Baernstein and J. Brown, Integral means of derivatives of monotone slit mappings, Comment. Math. Helv. 57 (1982), 331-348.
  • R.J. Bass, Integral representations of univalent functions and singular measures, Proc. Amer. Math. Soc. 110 (1990), 731-739.
  • C. Bennett and M. Stoll, Derivatives of analytic functions and bounded mean oscillation, Arch. Math. 47 (1986), 438-442.
  • A. Beurling, Ensembles exceptionnels, Acta Math. 72 (1940), 1-13.
  • O. Blasco, Operators on weighted Bergman spaces, $0<p\le1$, and applications, Duke Math. J. 66 (1992), 443-467.
  • O. Blasco, D. Girela and M.A. Márquez, Mean growth of the derivative of analytic functions, bounded mean oscillation and normal functions, Indiana Univ. Math. J. 47 (1998), 893-912.
  • O. Blasco and G. Soares de Souza, Spaces of analytic functions on the disc where the growth of $M_p(F,r)$ depends on a weight, J. Math. Anal. Appl. 147 (1990), 580-598.
  • S. Bloom and G. Soares de Souza, Weighted Lipschitz spaces and their analytic characterizations, Constr. Approx. 10 (1994), 339-376.
  • P. Bourdon, J. Shapiro and W. Sledd, Fourier series, mean Lipschitz spaces and bounded mean oscillation, Analysis at Urbana 1, Proc. of the Special Yr. in Modern Anal. at the Univ. of Illinois, 1986-87 (E.R. Berkson, N.T. Peck and J. Uhl, eds.), London Math. Soc. Lecture Notes Ser. 137, Cambridge Univ. Press, 1989, 81-110.
  • J.A. Cima and K.E. Petersen, Some analytic functions whose boundary values have bounded mean oscillation, Math. Z. 147 (1976), 237-347.
  • P.L. Duren, Theory of $H^p$ spaces, Academic Press, New York, 1970.
  • --------, Univalent functions, Springer-Verlag, New York, 1983.
  • M. Essén and J. Xiao, Some results on $Q_p$ spaces, $0<p<1$, J. Reine Angew. Math. 485 (1997), 173-195.
  • O. Frostman, Potential d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions 3, Meddel. Lunds Univ. Mat. Sem., 1935.
  • J.B. Garnett, Bounded analytic functions, Academic Press, New York, 1981.
  • D. Girela, On a theorem of Privalov and normal functions, Proc. Amer. Math. Soc. 125 (1997), 433-442.
  • --------, Mean Lipschitz spaces and bounded mean oscillation, Illinois J. Math. 41 (1997), 214-230.
  • G.H. Hardy and J.E. Littlewood, Some properties of fractional integrals, II, Math. Z. 34 (1932), 403-439.
  • J.P. Kahane and R. Salem, Ensembles parfaits et séries trigonométriques, Actualités Sci. Ind. No. 1301, Hermann, Paris, 1963.
  • G.D. Levshina, Coefficient multipliers of Lipschitz functions, Mat. Zametki 52 (1992), 68-77 (in Russian); Math. Notes 52 (1993), 1124-1130 (in English).
  • W. Rudin, The radial variation of analytic functions, Duke Math. J. 22 (1955), 235-242.
  • M. Tsuji, Potential theory in modern function theory, Chelsea Publ. Co., New York, 1975.
  • J.B. Twomey, Radial variation of functions in Dirichlet-type spaces, Mathematica 44 (1997), 267-277.
  • S. Yamashita, Gap series and $\a$-Bloch functions, Yokohama Math. J. 28 (1980), 31-36.
  • A. Zygmund, On certain integrals, Trans. Amer. Math. Soc. 55 (1944), 170-204.
  • --------, Trigonometric series, Vols. I and II, Cambridge Univ. Press, Cambridge, 1959.