Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups

Ewa Damek; Andrzej Hulanicki

Colloquium Mathematicae (1995)

  • Volume: 68, Issue: 1, page 121-140
  • ISSN: 0010-1354

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Damek, Ewa, and Hulanicki, Andrzej. "Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups." Colloquium Mathematicae 68.1 (1995): 121-140. <http://eudml.org/doc/210285>.

@article{Damek1995,
author = {Damek, Ewa, Hulanicki, Andrzej},
journal = {Colloquium Mathematicae},
keywords = {Fatou theorem; solvable Lie group; nilpotent Lie group; Abelian Lie group; Lie algebra; subelliptic operator; harmonic; probability measure; Poisson integral; admissible convergence; boundary; maximal function},
language = {eng},
number = {1},
pages = {121-140},
title = {Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups},
url = {http://eudml.org/doc/210285},
volume = {68},
year = {1995},
}

TY - JOUR
AU - Damek, Ewa
AU - Hulanicki, Andrzej
TI - Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups
JO - Colloquium Mathematicae
PY - 1995
VL - 68
IS - 1
SP - 121
EP - 140
LA - eng
KW - Fatou theorem; solvable Lie group; nilpotent Lie group; Abelian Lie group; Lie algebra; subelliptic operator; harmonic; probability measure; Poisson integral; admissible convergence; boundary; maximal function
UR - http://eudml.org/doc/210285
ER -

References

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  1. [Ch] M. Christ, Hilbert transforms along curves I. Nilpotent groups, Ann. of Math. (2) 122 (1985), 575-596. Zbl0593.43011
  2. [Chr] M. Christ, The strong maximal function on a nilpotent group, Trans. Amer. Math. Soc. 331 (1992), 1-13. Zbl0765.43002
  3. [CW] R. R. Coifman and G. Weiss, Operators associated with representations of amenable groups, singular integrals induced by ergodic flows, the rotations method and multipliers, Studia Math. 47 (1973), 285-303. Zbl0297.43010
  4. [D] E. Damek, Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups, ibid. 89 (1988), 169-196. Zbl0675.22005
  5. [DH] E. Damek and A. Hulanicki, Boundaries for left-invariant subelliptic operators on semi-direct products of nilpotent and abelian groups, J. Reine Angew. Math. 411 (1990), 1-38. Zbl0699.22012
  6. [K] A. Korányi, Harmonic functions on symmetric spaces, in: Symmetric Spaces, Birkhäuser, Basel, 1972, 379-412. Zbl0291.43016
  7. [NS] A. Nagel and E. M. Stein, On certain maximal functions and approach regions, Adv. in Math. 54 (1984), 83-106. Zbl0546.42017
  8. [R] F. Ricci, Singular integrals on ℝ n , Tempus lectures held at the Institute of Mathematics of Wrocław University, 1991. 
  9. [Sj] P. Sjögren, Admissible convergence of Poisson integrals in symmetric spaces, Ann. of Math. 124 (1986), 313-335. Zbl0646.31008
  10. [S] J. Sołowiej, The Fatou theorem for NA groups-a negative result, Colloq. Math. 67 (1994), 131-145. Zbl0839.22009
  11. [St] E. M. Stein, Boundary behavior of harmonic functions on symmetric spaces: Maximal estimates for Poisson integrals, Invent. Math. 74 (1983), 63-83. 

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