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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Oscillating multipliers on the Heisenberg group

### Tom 90 / 2001

Colloquium Mathematicum 90 (2001), 37-50 MSC: Primary 43A80, 43A22; Secondary 42C10, 22E30. DOI: 10.4064/cm90-1-3

#### Streszczenie

Let ${\cal L}$ be the sublaplacian on the Heisenberg group $H^n$. A recent result of Müller and Stein shows that the operator ${{\cal L}}^{-1/2} \mathop {\rm sin}\nolimits \sqrt{{\cal L}}$ 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.

#### Autorzy

• E. K. NarayananStatistics and Mathematics Division
Indian Statistical Institute
Bangalore 560 059, India
e-mail
• S. ThangaveluStatistics and Mathematics Division
Indian Statistical Institute