Hardy spaces on compact Lie groups

Brian E. Blank; Dashan Fan

Annales de la Faculté des sciences de Toulouse : Mathématiques (1997)

  • Volume: 6, Issue: 3, page 429-479
  • ISSN: 0240-2963

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Blank, Brian E., and Fan, Dashan. "Hardy spaces on compact Lie groups." Annales de la Faculté des sciences de Toulouse : Mathématiques 6.3 (1997): 429-479. <http://eudml.org/doc/73428>.

@article{Blank1997,
author = {Blank, Brian E., Fan, Dashan},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Hardy space; semisimple compact Lie group; maximal functions; Poisson kernel; unitary representation; heat kernel; maximal Bochner-Riesz operator; Dini condition},
language = {eng},
number = {3},
pages = {429-479},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Hardy spaces on compact Lie groups},
url = {http://eudml.org/doc/73428},
volume = {6},
year = {1997},
}

TY - JOUR
AU - Blank, Brian E.
AU - Fan, Dashan
TI - Hardy spaces on compact Lie groups
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1997
PB - UNIVERSITE PAUL SABATIER
VL - 6
IS - 3
SP - 429
EP - 479
LA - eng
KW - Hardy space; semisimple compact Lie group; maximal functions; Poisson kernel; unitary representation; heat kernel; maximal Bochner-Riesz operator; Dini condition
UR - http://eudml.org/doc/73428
ER -

References

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  2. [2] Caffarelli ( L.), Fabes ( E.), Mortola ( S.) and Salsa ( S.) .- Boundary behavior of nonnegative solutions of elliptic operators in divergence form, Indiana Univ. Math. J.30 (1981), pp. 621-640. Zbl0512.35038MR620271
  3. [3] Carleson ( L.) . — Two remarks on H1 and BMO, Advances in Math22 (1976), pp. 269-275. Zbl0357.46058MR477058
  4. [4] Clerc ( J-L.) .— Sommes de Riesz et multiplicateurs sur un groupe de Lie compact, Ann. Inst. Fourier24 (1974), pp. 149-172. Zbl0273.22011MR361620
  5. [5] Clerc ( J-L.) . — Bochner-Riesz means of Hp functions (0 &lt; p &lt; 1), in Lecture Notes in Mathematics1234 (1987), Springer-Verlag, New York, pp. 86-107. Zbl0625.43003
  6. [6] Coifman ( R.) .— A real variable characterization of Hp, Studia Math.51 (1974), pp. 269-274. Zbl0289.46037MR358318
  7. [7] Coifman ( R.) and Weiss ( G.) .— Extensions of Hardy space and their use in analysis, Bull. Amer. Math. Soc.83 (1977), pp. 569-645. Zbl0358.30023MR447954
  8. [8] Colzani ( L.) .— Hardy spaces on spheres, Ph. D. Dissertation, Washington University in St. Louis, 1982. 
  9. [9] Cowling ( M.), Mantero ( A.M.) and Ricci ( F.) .— Pointwise estimates for some kernels on compact Lie groups, Rend. Circ. Mat. PalermoXXXI, n° 2 (1982), pp. 145-158. Zbl0492.43006MR670392
  10. [10] Fan ( D.) Master Thesis, Anhui University, China. (1982). 
  11. [11] Fefferman ( C.) and Stein ( E.M.) .— Hp spaces of several variables, Acta Math.129 (1972), pp. 137-193. Zbl0257.46078MR447953
  12. [12] Folland ( G.B.) and Stein ( E.) .— Hardy Spaces on Homogeneous Groups, Princeton University Press, Princeton, New Jersey. 1982. Zbl0508.42025MR657581
  13. [13] Latter ( R.H.) .— A characterization of Hp (Rn) in terms of atoms, Studia Math.62 (1978), pp. 93-101. Zbl0398.42017MR482111
  14. [14] Stein ( E.M.) .— Topics in Harmonic Analysis, Ann. of Math. Studies63, Princeton Univ. Press, Princeton, New Jersey, 1970. Zbl0193.10502MR252961
  15. [15] Strichartz ( R.S.) . — Boundary values of solutions of elliptic equations satisfying Hp conditions, Trans. Amer. Math. Soc.176 (1973), pp. 445-462. Zbl0261.35042MR320525
  16. [16] Triebels ( W.) .— Some Fourier multiplier criteria and the spherical Bochner-Riesz, Rev. Roum. Math. Pures et Appl.XX, n° 10 (1975), pp. 1173-1185. Zbl0328.42003MR404967
  17. [17] Trudinger ( N.S.) .- Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations, Inventiones Math.61 (1980), pp. 67-79. Zbl0453.35028MR587334
  18. [18] Uchiyama ( A.) .— A maximal function characterization of Hp on the space of homogeneous type, Trans. Amer. Math. Soc.262 (1980), pp. 579-592. Zbl0503.46020MR586737

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