A multiplier theorem for H-type groups

Rita Pini

Studia Mathematica (1991)

  • Volume: 100, Issue: 1, page 39-49
  • ISSN: 0039-3223

Abstract

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We prove an L p -boundedness result for a convolution operator with rough kernel supported on a hyperplane of a group of Heisenberg type.

How to cite

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Pini, Rita. "A multiplier theorem for H-type groups." Studia Mathematica 100.1 (1991): 39-49. <http://eudml.org/doc/215872>.

@article{Pini1991,
abstract = {We prove an $L^p$-boundedness result for a convolution operator with rough kernel supported on a hyperplane of a group of Heisenberg type.},
author = {Pini, Rita},
journal = {Studia Mathematica},
keywords = {multipliers; singular integrals; Heisenberg group; -boundedness; convolution operators},
language = {eng},
number = {1},
pages = {39-49},
title = {A multiplier theorem for H-type groups},
url = {http://eudml.org/doc/215872},
volume = {100},
year = {1991},
}

TY - JOUR
AU - Pini, Rita
TI - A multiplier theorem for H-type groups
JO - Studia Mathematica
PY - 1991
VL - 100
IS - 1
SP - 39
EP - 49
AB - We prove an $L^p$-boundedness result for a convolution operator with rough kernel supported on a hyperplane of a group of Heisenberg type.
LA - eng
KW - multipliers; singular integrals; Heisenberg group; -boundedness; convolution operators
UR - http://eudml.org/doc/215872
ER -

References

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  1. [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, 1976. Zbl0344.46071
  2. [2] M. Christ, Hilbert transforms along curves. I. Nilpotent groups, Ann. of Math. 122 (1985), 575-596. Zbl0593.43011
  3. [3] R. R. Coifman and G. Weiss, Transference methods in harmonic analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., 1977. Zbl0371.43009
  4. [4] M. Cowling, A remark on twisted convolution, Suppl. Rend. Circ. Mat. Palermo 1 (1981). 203 209 
  5. [5] J. Cygan, Subadditivity of homogeneous norms on certain nilpotent Lie groups, Proc. Amer. Math. Soc. 83 (1981), 69-70. Zbl0475.43010
  6. [6] I. M. Gelfand and G. E. Shilov, Generalized Function I, Academic Press, 1964. 
  7. [7] D. Geller and E. M. Stein, Estimates for singular convolution operators on the Heisenberg group, Math. Ann. 267 (1984), 1-15. Zbl0537.43005
  8. [8] R. Goodman, Singular integral operators on nilpotent Lie groups, Ark. Mat. 18 (1980), 1-11. Zbl0449.43008
  9. [9] K. Hoffman and R. Kunze, Linear Algebra, Prentice-Hall, 1961. 
  10. [10] R. Howe, Quantum mechanics and partial differential operators, J. Funct. Anal. 38 (1980), 188-254. Zbl0449.35002
  11. [11] A. Kaplan, Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms, Trans. Amer. Math. Soc. 258 (1980), 147-153. Zbl0393.35015
  12. [12] A. Kaplan and F. Ricci, Harmonic analysis on groups of Heisenberg type, in: Lecture Notes in Math. 992, Springer, 1983, 416-435. 
  13. [13] D. Müller, Calderón-Zygmund kernels carried by linear subspaces of homogeneous nilpotent Lie algebras, invent. Math. 73 (1983), 467-489. Zbl0521.43009
  14. [14] D. Müller, Singular kernels supported by homogeneous submanifolds, J. Reine Angew. Math. 356 (1985), 90-118. Zbl0551.43005
  15. [15] F. Ricci, Calderón-Zygmund kernels on nilpotent Lie groups, in: Lecture Notes in Math. 908, Springer, 1982, 217-227. 
  16. [16] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. I. Oscillatory integrals, J. Funct. Anal. 73 (1987), 179-194. Zbl0622.42010
  17. [17] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. II. Singular kernels supported on submanifolds, ibid. 78 (1988), 56-84. Zbl0645.42019
  18. [18] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups. III. Fractional integration along manifolds, ibid. 86 (1989), 360-389. Zbl0684.22006
  19. [19] E. M. Stein and S. Wainger, Problems In harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), 1239-1295. Zbl0393.42010
  20. [20] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton 1975. Zbl0232.42007
  21. [21] R. Strichartz, Singular integrals on nilpotent Lie groups, Proc. Amer. Math. Soc. 53 (1975), 367-374. Zbl0322.43015

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