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Transactions of the American Mathematical Society

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On maximal functions and Poisson-Szegő integrals

Author: Juan Sueiro
Journal: Trans. Amer. Math. Soc. 298 (1986), 653-669
MSC: Primary 42B25; Secondary 32A40, 32M10
MathSciNet review: 860386
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Abstract: We study a class of maximal functions of Hardy-Littlewood type defined on spaces of homogeneous type and we give necessary and sufficient conditions for the corresponding maximal operators to be of weak type $ (1,1)$. As a consequence we show that Poisson-Szegö integrals of $ {L^p}$ functions possess certain boundary limits which are not implied by Korányi's theorem.

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  • [CW] R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certain espaces homogènes, Lecture Notes in Math., vol. 242, Springer-Verlag, Berlin, 1971. MR 0499948 (58:17690)
  • [FS] G. Folland and E. M. Stein, Estimates for the $ {\overline \partial _b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522. MR 0367477 (51:3719)
  • [HS] M. Hakim and N. Sibony, Fonctions holomorphes bornées et limites tangentielles, Duke Math. J. 50 (1983), 133-141. MR 700133 (84m:32011)
  • [K1] A. Korányi, The Poisson integral for generalized half-planes and bounded symmetric domains, Ann. of Math. (2) 82 (1965), 332-350. MR 0200478 (34:371)
  • [K2] -, Harmonic functions on hermitian hyperbolic space, Trans. Amer. Math. Soc. 135 (1969), 507-516. MR 0277747 (43:3480)
  • [KV] A. Korányi and S. Vági, Singular integrals on homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa 25 (1971), 575-648. MR 0463513 (57:3462)
  • [L] J. E. Littlewood, On a theorem of Fatou, J. London Math. Soc. 2 (1927), 172-176.
  • [NS] A. Nagel and E. M. Stein, On certain maximal functions and approach regions, Adv. in Math. 54 (1984), 83-106. MR 761764 (86a:42026)
  • [S] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N.J., 1970. MR 0290095 (44:7280)
  • [SW] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, N.J., 1971. MR 0304972 (46:4102)
  • [Su] J. Sueiro, A note on maximal operators of Hardy Littlewood type (to appear). MR 886442 (88e:42037)
  • [Z] A. Zygmund, On a theorem of Littlewood, Summa Brasil. Math. 2 (1949), 1-7. MR 0036306 (12:88c)

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Article copyright: © Copyright 1986 American Mathematical Society

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