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1991 | 100 | 1 | 39-49
Tytuł artykułu

A multiplier theorem for H-type groups

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove an $L^p$-boundedness result for a convolution operator with rough kernel supported on a hyperplane of a group of Heisenberg type.
Słowa kluczowe
Czasopismo
Rocznik
Tom
100
Numer
1
Strony
39-49
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-07-05
poprawiono
1990-12-03
Twórcy
autor
  • Dipartimento di Matematica, Universitá di Verona, Via dell'Artigliere 19, 37129 Verona, Italy
Bibliografia
  • [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, 1976.
  • [2] M. Christ, Hilbert transforms along curves. I. Nilpotent groups, Ann. of Math. 122 (1985), 575-596.
  • [3] R. R. Coifman and G. Weiss, Transference methods in harmonic analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., 1977.
  • [4] M. Cowling, A remark on twisted convolution, Suppl. Rend. Circ. Mat. Palermo 1 (1981). 203 209
  • [5] J. Cygan, Subadditivity of homogeneous norms on certain nilpotent Lie groups, Proc. Amer. Math. Soc. 83 (1981), 69-70.
  • [6] I. M. Gelfand and G. E. Shilov, Generalized Function I, Academic Press, 1964.
  • [7] D. Geller and E. M. Stein, Estimates for singular convolution operators on the Heisenberg group, Math. Ann. 267 (1984), 1-15.
  • [8] R. Goodman, Singular integral operators on nilpotent Lie groups, Ark. Mat. 18 (1980), 1-11.
  • [9] K. Hoffman and R. Kunze, Linear Algebra, Prentice-Hall, 1961.
  • [10] R. Howe, Quantum mechanics and partial differential operators, J. Funct. Anal. 38 (1980), 188-254.
  • [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.
  • [12] A. Kaplan and F. Ricci, Harmonic analysis on groups of Heisenberg type, in: Lecture Notes in Math. 992, Springer, 1983, 416-435.
  • [13] D. Müller, Calderón-Zygmund kernels carried by linear subspaces of homogeneous nilpotent Lie algebras, invent. Math. 73 (1983), 467-489.
  • [14] D. Müller, Singular kernels supported by homogeneous submanifolds, J. Reine Angew. Math. 356 (1985), 90-118.
  • [15] F. Ricci, Calderón-Zygmund kernels on nilpotent Lie groups, in: Lecture Notes in Math. 908, Springer, 1982, 217-227.
  • [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.
  • [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.
  • [18] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups. III. Fractional integration along manifolds, ibid. 86 (1989), 360-389.
  • [19] E. M. Stein and S. Wainger, Problems In harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), 1239-1295.
  • [20] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton 1975.
  • [21] R. Strichartz, Singular integrals on nilpotent Lie groups, Proc. Amer. Math. Soc. 53 (1975), 367-374.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv100i1p39bwm
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