JournalsrmiVol. 11, No. 2pp. 269–308

LpL^p multipliers and their H1H^1-L1L^1 estimates on the Heisenberg group

  • Chincheng Lin

    National Central University, Chung-Li, Taiwan
$L^p$ multipliers and their $H^1$-$L^1$ estimates on the Heisenberg group cover
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Abstract

We give a Hörmander-type sufficient condition on an operator-valued function MM that implies the LpL^p-boundedness result for the operator TMT_M defined by (T_Mf^ = Mf^M\hat{f} on the (2n+1)(2n + 1)- dimensional Heisenberg group Hn\mathbb H^n. Here "^" denotes the Fourier transform on Hn\mathbb H^n defined in terms of the Fock representations. We also show the H1H^1-L1L^1-boundedness of TMT_M. TMfL1CfH1\|T_Mf\|_{L^1} ≤C \|f\|_{H^1}, for Hn\mathbb H^n under the same hypotheses of LpL^p-boundedness.

Cite this article

Chincheng Lin, LpL^p multipliers and their H1H^1-L1L^1 estimates on the Heisenberg group. Rev. Mat. Iberoam. 11 (1995), no. 2, pp. 269–308

DOI 10.4171/RMI/173