Boundedness of some multipliers on stratified Lie groups

Abstract

Let £ be the sub-Laplacian on a stratified Lie group G, and let m be a function defined on [0,+\infty). We give the boundedness of the multiplier operators m(£) on Herz-type Hardy spaces on G.

Keywords

Stratified group / Herz-type Hardy space / multiplier

References

[1] De Michele L, Mauceri G. L^p-multipliers on the Heisenberg group. Michigan Math J, 1979, 26: 371-373

[2] De Michele L, Mauceri G. H^p-multipliers on stratified groups. Ann Mat Pura Appl, 1987, 148: 353-366

[3] Fefferman C, Stein E M. H^p space of several variables. Acta Math, 1972, 129: 137-193

[4] Folland G B, Stein E M. Hardy Spaces on Homogeneous Groups. Math Notes, 28. Princeton: Princeton Univ Press, 1982

[5] Jiang Y S, Tang L. Decompositions of Herz-type hardy spaces on homogeneous groups. Adv Math China, 2006, 35: 366-374

[6] Mauceri G. Maximal operators and Riesz means on stratified groups. Symposia Math, 1987, 29: 47-62

[7] Mauceri G, Meda S. Vector-valued multipliers on stratified groups. Rev Mat Iberoam, 1990, 6: 141-154

[8] Miyachi A. On some Fourier multipliers for H^p(ℝn). J Fac Sci Univ Tokyo, 1980, 27: 157-179

[9] Peral J. L^p estimates for the wave equations. J Funct Anal, 1980, 36: 114-145

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Higher Education Press and Springer-Verlag Berlin Heidelberg