Lp multipliers and their H1-L1 estimates on the Heisenberg group.

Lin, Chin-Cheng. "Lp multipliers and their H1-L1 estimates on the Heisenberg group.." Revista Matemática Iberoamericana 11.2 (1995): 269-308. <http://eudml.org/doc/39477>.

@article{Lin1995,
abstract = {We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.},
author = {Lin, Chin-Cheng},
journal = {Revista Matemática Iberoamericana},
keywords = {Algebra de operadores; Teoría de grupos; Multiplicadores; Transformada de Fourier; Problemas de valor acotado; multipliers; Heisenberg group; Fourier transform; Fock representations},
language = {eng},
number = {2},
pages = {269-308},
title = {Lp multipliers and their H1-L1 estimates on the Heisenberg group.},
url = {http://eudml.org/doc/39477},
volume = {11},
year = {1995},
}

TY - JOUR
AU - Lin, Chin-Cheng
TI - Lp multipliers and their H1-L1 estimates on the Heisenberg group.
JO - Revista Matemática Iberoamericana
PY - 1995
VL - 11
IS - 2
SP - 269
EP - 308
AB - We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.
LA - eng
KW - Algebra de operadores; Teoría de grupos; Multiplicadores; Transformada de Fourier; Problemas de valor acotado; multipliers; Heisenberg group; Fourier transform; Fock representations
UR - http://eudml.org/doc/39477
ER -