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References
[C] Christ, M.:L p bounds for spectral multipliers on nilpotent Lie groups. Trans. Am. Math. Soc.328 (1991) 73–81
[CF] Chang, S.Y., Fefferman, R.: Some recent developments in Fourier analysis andH p theory on product domains. Bull. Am. Math. Soc.12 (1985) 1–43
[CW] Coifman, R.R.; Weiss, G.: Transference Methods in Analysis. CBMS Reg. Conf. Series in Math., Vol. 31, Am. Math. Soc., 1977
[E] Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions, II, McGraw-Hill, New York, 1953
[Fe] Fefferman, R.: Harmonic analysis of operators associated with a multiparameter group of dilations (preprint)
[FeS] Fefferman, C., Stein, E.M.: Some maximal inequalities. Am. J. Math.93 (1971) 107–115
[FoS] Folland, G., Stein, E.M.: Hardy Spaces on Homogenous Groups. Princeton Univ. Press, Princeton, N.J., 1982
[G] Geller, D.: Fourier analysis on the heisenberg group. Proc. Natl. Acad. Sci. USA74 (1977) 1328–1331
[H] Hebisch, W.: Multiplier theorem on generalized Heisenberg groups. Coll. Math.65 (1993) 231–239
[J] Journé, J.L.: Calderón-Zygmund operators on product spaces. Rev. Mat. Iberoam.1 (1985) 55–92
[M] Mauceri, G.: Zonal multipliers on the Heisenberg group. Pacific J. Math.95 (1981) 143–159
[MM] Mauceri, G., Meda, S.: Vector-valued multipliers on stratified groups. Rev. Mat. Iberoamer.6 (1990) 141–154
[MRS] Müller, D., Ricci, F., Stein, E.M.: Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups, II Math. Z. (to appear)
[MS] Müller, D., Stein, E.M.: On spectral multipliers for Heisenberg and related groups. J. Math. Pures Appl.73 (1994) 413–440
[NRS] Nagel, A., Ricci, F., Stein, E.M.: Harmonic analysis and fundamental solutions on nilpotent Lie groups) In: Analysis and Partial Differential Equations. Cora Sadosky (ed). Lecture Notes in Pure Appl. Math., M. Dekker NY122 (1990) 249–275
[PS] Phong, D.H., Stein, E.M.: Some further classes of pseudo-differential and singular-integral operators arising in boundary value problems, I. Composition of operators. Am. J. Math.104 (1982) 141–172
[RS] Ricci, F., Stein, E.M.: Multiparameter singular integrals and maximal functions. Ann. Inst. Fourier Gren.42 (1992) 637–670
[S1] Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, NJ, 1970
[S2] Stein, E.M.: Harmonic Analysis, Princeton University Press, Princeton, NJ, 1993
[S] Strichartz, R.:L p-harmonic analysis and Radon transforms on the Heisenberg group. J. Funct. Anal.96 (1991) 350–406
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Oblatum 3-I-1994 & 1-VI-1994
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Müller, D., Ricci, F. & Stein, E.M. Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups, I. Invent Math 119, 199–233 (1995). https://doi.org/10.1007/BF01245180
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DOI: https://doi.org/10.1007/BF01245180