Project Euclid

References

• [1] J. M. Anderson and L. D. Pitt, Probabilistic behavior of functions in the Zygmund spaces $\Lambda^\ast$ and $\lambda^\ast$, preprint.
  Mathematical Reviews (MathSciNet): MR1014871
  Zentralblatt MATH: 0739.42007
  Digital Object Identifier: doi:10.1112/plms/s3-59.3.558
  
• [2] R. Bañuelos, Brownian motion and area functions, Indiana Univ. Math. J. 35 (1986), no. 3, 643–668.
  Mathematical Reviews (MathSciNet): MR87k:60126
  Zentralblatt MATH: 0624.60058
  Digital Object Identifier: doi:10.1512/iumj.1986.35.35034
  
• [3] R. Bañuelos and C. N. Moore, Some results in analysis related to the law of the iterated logarithm, Proc. Special Year in Analysis, University of Illinois, to appear.
• [4] R. Bañuelos and C. N. Moore, Sharp estimates for the nontangential maximal function and the Lusin area function, to appear in Trans. Amer. Math. Soc.
• [5] N. H. Bingham, Variants on the law of the iterated logarithm, Bull. London Math. Soc. 18 (1986), no. 5, 433–467.
  Mathematical Reviews (MathSciNet): MR87k:60087
  Zentralblatt MATH: 0633.60042
  Digital Object Identifier: doi:10.1112/blms/18.5.433
  
• [6]¹ A.-P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution, Advances in Math. 16 (1975), 1–64.
  Mathematical Reviews (MathSciNet): MR54:5736
  Zentralblatt MATH: 0315.46037
  Digital Object Identifier: doi:10.1016/0001-8708(75)90099-7
  
• [6]² A.-P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution. II, Advances in Math. 24 (1977), no. 2, 101–171.
  Mathematical Reviews (MathSciNet): MR56:9180
  Zentralblatt MATH: 0355.46021
  Digital Object Identifier: doi:10.1016/S0001-8708(77)80016-9
  
• [7] S.-Y. A. Chang, J. M. Wilson, and T. H. Wolff, Some weighted norm inequalities concerning the Schrödinger operators, Comment. Math. Helv. 60 (1985), no. 2, 217–246.
  Mathematical Reviews (MathSciNet): MR87d:42027
  Zentralblatt MATH: 0575.42025
  Digital Object Identifier: doi:10.1007/BF02567411
  
• [8] K. L. Chung, On the maximum partial sums of sequences of independent random variables, Trans. Amer. Math. Soc. 64 (1948), 205–233.
  Mathematical Reviews (MathSciNet): MR10,132b
  Zentralblatt MATH: 0032.17102
  Digital Object Identifier: doi:10.2307/1990499
  JSTOR: links.jstor.org
  
• [9] K. L. Chung, A Course in Probability Theory, 2nd ed., Academic Press, New York-London, 1974.
  Mathematical Reviews (MathSciNet): MR49:11579
  Zentralblatt MATH: 0345.60003
  
• [10] R. Durrett, Brownian motion and martingales in analysis, Wadsworth Mathematics Series, Wadsworth International Group, Belmont, CA, 1984.
  Mathematical Reviews (MathSciNet): MR87a:60054
  Zentralblatt MATH: 0554.60075
  
• [11] P. Erdös and I. S. Gál, On the law of the iterated logarithm. I, II, Nederl. Akad. Wetensch. Proc. Ser. A. 58 = Indag. Math. 17 (1955), 65–76, 77–84.
  Mathematical Reviews (MathSciNet): MR16,1016g
  Zentralblatt MATH: 0068.05403
  
• [12] J. B. Garnett, Bounded Analytic Functions, Pure and Applied Mathematics, vol. 96, Academic Press, New York, 1981.
  Mathematical Reviews (MathSciNet): MR83g:30037
  Zentralblatt MATH: 0469.30024
  
• [13] R. F. Gundy, The martingale version of a theorem of Marcinkiewicz and Zygmund, Ann. Math. Statist 38 (1967), 725–734.
  Mathematical Reviews (MathSciNet): MR35:6194
  Zentralblatt MATH: 0153.20901
  Digital Object Identifier: doi:10.1214/aoms/1177698865
  Project Euclid: euclid.aoms/1177698865
  
• [14] R. F. Gundy, The density of the area integral, Conference on Harmonic Analysis in Honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) eds. W. Beckner, A. Calderón, R. Fefferman, and P. Jones, Wadsworth Math. Ser., Wadsworth, Belmont, California, 1983, pp. 138–149.
  Mathematical Reviews (MathSciNet): MR85k:42048
  Zentralblatt MATH: 0544.31012
  
• [15] R. F. Gundy and M. L. Silverstein, The density of the area integral in $\bf R\sp n+1\sb +$, Ann. Inst. Fourier (Grenoble) 35 (1985), no. 1, 215–229.
  Mathematical Reviews (MathSciNet): MR86e:26012
  Zentralblatt MATH: 0544.31012
  
• [16] D. S. Jerison and C. E. Kenig, Boundary behavior of harmonic functions in nontangentially accessible domains, Adv. in Math. 46 (1982), no. 1, 80–147.
  Mathematical Reviews (MathSciNet): MR84d:31005b
  Zentralblatt MATH: 0514.31003
  Digital Object Identifier: doi:10.1016/0001-8708(82)90055-X
  
• [17] C. E. Kenig, Weighted $H\spp$ spaces on Lipschitz domains, Amer. J. Math. 102 (1980), no. 1, 129–163.
  Mathematical Reviews (MathSciNet): MR81d:30060
  Zentralblatt MATH: 0434.42024
  Digital Object Identifier: doi:10.2307/2374173
  JSTOR: links.jstor.org
  
• [18] H. Kesten, An iterated logarithm law for local time, Duke Math. J. 32 (1965), 447–456.
  Mathematical Reviews (MathSciNet): MR31:2751
  Zentralblatt MATH: 0132.12701
  Digital Object Identifier: doi:10.1215/S0012-7094-65-03245-X
  Project Euclid: euclid.dmj/1077375916
  
• [19] N. Kolmogorov, Über des Gesetz des iterieten logarithmus, Math. Ann. 101 (1929), 126–139.
• [20] N. G. Makarov, On the distortion of boundary sets under conformal mappings, Proc. London Math. Soc. (3) 51 (1985), no. 2, 369–384.
  Mathematical Reviews (MathSciNet): MR87d:30012
  Zentralblatt MATH: 0573.30029
  Digital Object Identifier: doi:10.1112/plms/s3-51.2.369
  
• [21] C. N. Moore, Some applications of Cauchy integrals on curves, dissertation, University of California, Los Angeles, 1986.
• [22] T. Murai and A. Uchiyama, Good $\lambda$ inequalities for the area integral and the nontangential maximal function, Studia Math. 83 (1986), no. 3, 251–262.
  Mathematical Reviews (MathSciNet): MR87m:42016
  Zentralblatt MATH: 0611.42010
  
• [23] W. Philipp and W. Stout, Almost sure invariance principles for partial sums of weakly dependent random variables, Mem. Amer. Math. Soc. 161 (1975), no. issue 2, 161, iv+140, American Mathematical Society, Providence, Rhode Island.
  Mathematical Reviews (MathSciNet): MR55:6570
  Zentralblatt MATH: 0361.60007
  
• [24] W. Philipp and W. Stout, Invariance principles for martingales and sums of independent random variables, Math. Z. 192 (1986), no. 2, 253–264.
  Mathematical Reviews (MathSciNet): MR88c:60094
  Zentralblatt MATH: 0601.60033
  Digital Object Identifier: doi:10.1007/BF01179427
  
• [25] P. Przytycki, On the law of iterated logarithm for Bloch functions, preprint.
• [26] R. Salem and A. Zygmund, La loi du logarithme itéré pour les séries trigonométriques lacunaires, Bull. Sci. Math. (2) 74 (1950), 209–224.
  Mathematical Reviews (MathSciNet): MR12,605c
  Zentralblatt MATH: 0039.07001
  
• [27] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, New Jersey, 1970.
  Mathematical Reviews (MathSciNet): MR44:7280
  Zentralblatt MATH: 0207.13501
  
• [28] W. Stout, A martingale analogue of Kolmogorov's law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 15 (1970), 279–290.
  Mathematical Reviews (MathSciNet): MR45:2778
  Zentralblatt MATH: 0209.49004
  Digital Object Identifier: doi:10.1007/BF00533299
  
• [29] V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 211–226 (1964).
  Mathematical Reviews (MathSciNet): MR30:5379
  Zentralblatt MATH: 0132.12903
  Digital Object Identifier: doi:10.1007/BF00534910
  
• [30] S. Takahashi, Almost sure invariance principles for lacunary trigonometric series, Tôhoku Math. J. (2) 31 (1979), no. 4, 439–451.
  Mathematical Reviews (MathSciNet): MR81c:60041
  Zentralblatt MATH: 0407.60022
  Digital Object Identifier: doi:10.2748/tmj/1178229729
  Project Euclid: euclid.tmj/1178229729
  
• [31] M. Weiss, The law of the iterated logarithm for lacunary trigonometric series. , Trans. Amer. Math. Soc. 91 (1959), 444–469.
  Mathematical Reviews (MathSciNet): MR21:7396
  Zentralblatt MATH: 0143.28801
  Digital Object Identifier: doi:10.2307/1993258
  JSTOR: links.jstor.org