The Fatou theorem for NA groups - a negative result

Jarosław Sołowiej

Colloquium Mathematicae (1994)

  • Volume: 67, Issue: 1, page 131-145
  • ISSN: 0010-1354

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Sołowiej, Jarosław. "The Fatou theorem for NA groups - a negative result." Colloquium Mathematicae 67.1 (1994): 131-145. <http://eudml.org/doc/210256>.

@article{Sołowiej1994,
author = {Sołowiej, Jarosław},
journal = {Colloquium Mathematicae},
keywords = {Fatou theorem; homogeneous Lie group; Poisson integral; solvable groups; nilpotent Lie group; Abelian Lie group; subelliptic operator; Lie algebra; probability measure; harmonic function; admissible convergence; boundary},
language = {eng},
number = {1},
pages = {131-145},
title = {The Fatou theorem for NA groups - a negative result},
url = {http://eudml.org/doc/210256},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Sołowiej, Jarosław
TI - The Fatou theorem for NA groups - a negative result
JO - Colloquium Mathematicae
PY - 1994
VL - 67
IS - 1
SP - 131
EP - 145
LA - eng
KW - Fatou theorem; homogeneous Lie group; Poisson integral; solvable groups; nilpotent Lie group; Abelian Lie group; subelliptic operator; Lie algebra; probability measure; harmonic function; admissible convergence; boundary
UR - http://eudml.org/doc/210256
ER -

References

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  1. [Br] L. R. Bragg, Hypergeometric operator series and related partial differential equations, Trans. Amer. Math. Soc. 143 (1969), 319-336. Zbl0195.10803
  2. [D] E. Damek, Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups, Studia Math. 89 (1988), 169-196. Zbl0675.22005
  3. [DH1] E. Damek and A. Hulanicki, Boundaries for left-invariant subelliptic operators on semidirect products of nilpotent and abelian groups, J. Reine Angew. Math. 411 (1990), 1-38. Zbl0699.22012
  4. [DH2] E. Damek and A. Hulanicki, Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group, Studia Math. 101 (1991), 34-68. Zbl0811.43001
  5. [DH3] E. Damek and A. Hulanicki, Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups, ibid., to appear. Zbl0839.22008
  6. [FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, 1982. Zbl0508.42025
  7. [G] M. de Guzmán, Differentiation of Integrals in R n , Lecture Notes in Math. 481, Springer, 1975. Zbl0327.26010
  8. [H1] A. Hulanicki, Subalgebra of L 1 ( G ) associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287. Zbl0316.43005
  9. [H2] A. Hulanicki, A class of convolution semi-groups of measures on a Lie group, in: Lecture Notes in Math. 828, Springer, 1980, 82-101. 
  10. [Sch] I. J. Schoenberg, On the Besicovitch-Perron solution of the Kakeya problem, in: Studies in Mathematical Analysis and Related Topics, G. Szegö et al. (eds.), Stanford Univ. Press, 1962, 359-363. 
  11. [SW] E. M. Stein and N. J. Weiss, On the convergence of Poisson integrals, Trans. Amer. Math. Soc. 140 (1969), 35-54. Zbl0182.10801

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