Oscillating multipliers on the Heisenberg group

E. K. Narayanan; S. Thangavelu

Colloquium Mathematicae, Tome 89 (2001), p. 37-50 / Harvested from The Polish Digital Mathematics Library

Résumé

Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator $ℒ^{- 1 / 2} s i n \sqrt ℒ$ is bounded on $L^{p} (H ⁿ)$ for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on $L^{p}$ in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.

Publié le : 2001-01-01

Zbl 0996.43012

EUDML-ID : urn:eudml:doc:284281

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-1-3,
     author = {E. K. Narayanan and S. Thangavelu},
     title = {Oscillating multipliers on the Heisenberg group},
     journal = {Colloquium Mathematicae},
     volume = {89},
     year = {2001},
     pages = {37-50},
     zbl = {0996.43012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-1-3}
}

E. K. Narayanan; S. Thangavelu. Oscillating multipliers on the Heisenberg group. Colloquium Mathematicae, Tome 89 (2001) pp. 37-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-1-3/