no. 4
A value-distribution criterion for the class L log L and some related questions
Annales de l'Institut Fourier, Tome 35 (1985) no. 4, pp. 127-150.
corrigé par Erratum : A value-distribution criterion for the class L log L and some related questions

Nous donnons une condition nécessaire et suffisante pour qu’une fonction analytique dans H 1 ait une partie réelle dans la classe L logL. Cette condition généralise la condition classique de Zygmund ; on donne aussi d’autres conditions suffisantes.

We give a necessary and sufficient condition for an analytic function in H 1 to have real part in class L logL. This condition contains the classical one of Zygmund; other variants are also given.

@article{AIF_1985__35_4_127_0,
     author = {Essen, M. and Shea, D. F. and Stanton, C. S.},
     title = {A value-distribution criterion for the class $L~{\rm log} L$ and some related questions},
     journal = {Annales de l'Institut Fourier},
     pages = {127--150},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {35},
     number = {4},
     year = {1985},
     doi = {10.5802/aif.1030},
     zbl = {0563.30025},
     mrnumber = {87e:30041},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1030/}
}
TY  - JOUR
AU  - Essen, M.
AU  - Shea, D. F.
AU  - Stanton, C. S.
TI  - A value-distribution criterion for the class $L~{\rm log} L$ and some related questions
JO  - Annales de l'Institut Fourier
PY  - 1985
SP  - 127
EP  - 150
VL  - 35
IS  - 4
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1030/
DO  - 10.5802/aif.1030
LA  - en
ID  - AIF_1985__35_4_127_0
ER  - 
%0 Journal Article
%A Essen, M.
%A Shea, D. F.
%A Stanton, C. S.
%T A value-distribution criterion for the class $L~{\rm log} L$ and some related questions
%J Annales de l'Institut Fourier
%D 1985
%P 127-150
%V 35
%N 4
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1030/
%R 10.5802/aif.1030
%G en
%F AIF_1985__35_4_127_0
Essen, M.; Shea, D. F.; Stanton, C. S. A value-distribution criterion for the class $L~{\rm log} L$ and some related questions. Annales de l'Institut Fourier, Tome 35 (1985) no. 4, pp. 127-150. doi : 10.5802/aif.1030. https://aif.centre-mersenne.org/articles/10.5802/aif.1030/

[1] A. Baernstein, Integral means, univalent functions and circular symmetrization, Acta Math., 133 (1974), 133-169. | MR | Zbl

[2] A. Baernstein, Some sharp inequalities for conjugate functions, Indiana Univ. Math. J., 27 (1978), 833-852. | MR | Zbl

[3] M. Benedicks, Positive harmonic functions vanishing on the boundary of certain domains in Rn, Ark. f. Mat., 18 (1980), 53-72. | MR | Zbl

[4] D. L. Burkholder, Exit times of Brownian motion, harmonic majorization, and Hardy spaces, Advances in Math., 26 (1977), 182-205. | MR | Zbl

[5] D. L. Burkholder, Brownian Motion and the Hardy Spaces Hp, in Aspects of Contemporary Complex Analysis, editors Brannan and Clunie, Academic Press 1980, 97-118. | MR | Zbl

[6] P. Duren, Theory of Hp-spaces, Academic Press, 1970. | MR | Zbl

[7] M. Essén and D. F. Shea, On some questions of uniqueness in the theory of symmetrization, Ann. Acad. Sci. Fennicae, Series A. I. Math., 4 (1978/1979), 311-340. | MR | Zbl

[8] M. Essén and D. F. Shea, Some recent results on conjugate functions in the unit disk. Proc. of the 18th Scand. Congress of Mathematicians, 1980, Progress in Mathematics, Vol. 11, Birkhäuser. | Zbl

[8a] M. Essén and K. Haliste, J. L. Lewis and D.F. Shea, Harmonic Majorization and classical analysis, J. London Math. Soc. (to appear). | Zbl

[9] K. Haliste, Estimates of harmonic measure, Ark. f. Mat., 6 (1965), 1-31. | MR | Zbl

[10] K. Haliste, Harmonic Majorization, Report No. 5 (1982), Department of Mathematics, University of Umeå, Sweden.

[11] W. K. Hayman, Meromorphic Functions, Oxford University Press, 1964. | MR | Zbl

[12] W. K. Hayman and P. B. Kennedy, Subharmonic Functions, vol. 1, Academic Press, 1976. | MR | Zbl

[13] W. K. Hayman and Ch. Pommerenke, On analytic functions of bounded mean oscillation, Bull. London Math. Soc., 10 (1978), 219-224. | MR | Zbl

[14] W. K. Hayman and A. Weitsman, On the coefficients of functions omitting values, Math. Proc. Cambridge Philos. Soc., 77 (1975), 119-137. | MR | Zbl

[15] O. Lehto, A majorant principle in the theory of functions, Math. Scand., 1 (1953), 5-17. | MR | Zbl

[16] R. Nevanlinna, Analytic functions, Springer-Verlag, 1970. | Zbl

[17] K. E. Petersen, Brownian motion, Hardy spaces and Bounded Mean Oscillation, London Math. Soc. Lecture Note Series, 28 (1977). | MR | Zbl

[18] L. I. Ronkin, Introduction to the theory of entire functions of several complex variables, Transl. Math. Monographs, Vol. 44, Amer. Math. Soc., Providence, R. I. 1974. | MR | Zbl

[19] C. S. Stanton, Riesz mass and growth problems for subharmonic functions, Thesis, University of Wisconsin 1982.

[20] W. Stoll, About entire and meromorphic functions of exponential type, Proc. of Symp. in Pure Math., Vol. XI, Amer. Math. Soc., Providence, R.I. 1968, 392-430. | MR | Zbl

[21] M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo 1959. | MR | Zbl

[22] A. Zygmund, Sur les fonctions conjuguées, Fund. Math., 13 (1929), 284-303. | JFM

Cité par Sources :