A value-distribution criterion for the class $L\log L$ and some related questions

 Access to full text

 Full (PDF)

1. [1] A. BAERNSTEIN, Integral means, univalent functions and circular symmetrization, Acta Math., 133 (1974), 133-169. Zbl0315.30021MR54 #5456
2. [2] A. BAERNSTEIN, Some sharp inequalities for conjugate functions, Indiana Univ. Math. J., 27 (1978), 833-852. Zbl0372.42007MR80g:30022
3. [3] M. BENEDICKS, Positive harmonic functions vanishing on the boundary of certain domains in Rn, Ark. f. Mat., 18 (1980), 53-72. Zbl0455.31009MR82h:31004
4. [4] D. L. BURKHOLDER, Exit times of Brownian motion, harmonic majorization, and Hardy spaces, Advances in Math., 26 (1977), 182-205. Zbl0372.60112MR57 #14163
5. [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. Zbl0497.30028MR84a:30061
6. [6] P. DUREN, Theory of Hp-spaces, Academic Press, 1970. Zbl0215.20203MR42 #3552
7. [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. Zbl0392.31001MR81d:30002
8. [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. Zbl0462.30025
9. [8a] M. ESSÉN and K. HALISTE, J. L. LEWIS and D.F. SHEA, Harmonic Majorization and classical analysis, J. London Math. Soc. (to appear). Zbl0558.30027
10. [9] K. HALISTE, Estimates of harmonic measure, Ark. f. Mat., 6 (1965), 1-31. Zbl0178.13801MR34 #1547
11. [10] K. HALISTE, Harmonic Majorization, Report No. 5 (1982), Department of Mathematics, University of Umeå, Sweden. 
12. [11] W. K. HAYMAN, Meromorphic Functions, Oxford University Press, 1964. Zbl0115.06203MR29 #1337
13. [12] W. K. HAYMAN and P. B. KENNEDY, Subharmonic Functions, vol. 1, Academic Press, 1976. Zbl0419.31001MR57 #665
14. [13] W. K. HAYMAN and Ch. POMMERENKE, On analytic functions of bounded mean oscillation, Bull. London Math. Soc., 10 (1978), 219-224. Zbl0386.30011MR81g:30044
15. [14] W. K. HAYMAN and A. WEITSMAN, On the coefficients of functions omitting values, Math. Proc. Cambridge Philos. Soc., 77 (1975), 119-137. Zbl0301.30011MR50 #13495
16. [15] O. LEHTO, A majorant principle in the theory of functions, Math. Scand., 1 (1953), 5-17. Zbl0051.05906MR15,115d
17. [16] R. NEVANLINNA, Analytic functions, Springer-Verlag, 1970. Zbl0199.12501
18. [17] K. E. PETERSEN, Brownian motion, Hardy spaces and Bounded Mean Oscillation, London Math. Soc. Lecture Note Series, 28 (1977). Zbl0363.60004MR58 #31383
19. [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. Zbl0286.32004MR49 #10901
20. [19] C. S. STANTON, Riesz mass and growth problems for subharmonic functions, Thesis, University of Wisconsin 1982. 
21. [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. Zbl0177.34201MR38 #4706
22. [21] M. TSUJI, Potential theory in modern function theory, Maruzen, Tokyo 1959. Zbl0087.28401MR22 #5712
23. [22] A. ZYGMUND, Sur les fonctions conjuguées, Fund. Math., 13 (1929), 284-303. Zbl55.0751.02JFM55.0751.02

1. Matts Essén, Daniel F. Shea, Charles S. Stanton, Sharp $L{\log }^{\alpha }L$ inequalities for conjugate functions