# The Fatou theorem for NA groups - a negative result

Colloquium Mathematicae (1994)

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

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topSołowiej, 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

top- [Br] L. R. Bragg, Hypergeometric operator series and related partial differential equations, Trans. Amer. Math. Soc. 143 (1969), 319-336. Zbl0195.10803
- [D] E. Damek, Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups, Studia Math. 89 (1988), 169-196. Zbl0675.22005
- [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
- [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
- [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
- [FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, 1982. Zbl0508.42025
- [G] M. de Guzmán, Differentiation of Integrals in ${R}^{n}$, Lecture Notes in Math. 481, Springer, 1975. Zbl0327.26010
- [H1] A. Hulanicki, Subalgebra of ${L}_{1}\left(G\right)$ associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287. Zbl0316.43005
- [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.
- [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.
- [SW] E. M. Stein and N. J. Weiss, On the convergence of Poisson integrals, Trans. Amer. Math. Soc. 140 (1969), 35-54. Zbl0182.10801

## Citations in EuDML Documents

top- Ewa Damek, Andrzej Hulanicki, Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups
- Andrzej Hulanicki, Estimates for the Poisson kernels and a Fatou type theorem applications to analysis on Siegel domains
- Ewa Damek, Pointwise estimates for the Poisson kernel on NA groups by the Ancona method
- Ewa Damek, Andrzej Hulanicki, Jacek Zienkiewicz, Estimates for the Poisson kernels and their derivatives on rank one NA groups

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