IJPAM: Volume 34, No. 4 (2007)

CHARACTERISATION OF $L^1-L^p$ MULTIPLIERS
FOR THE HEISENBERG GROUP

Swain Jitendriya$^1$, Ramakrishnan Radha$^2$
$^{1,2}$Department of Mathematics
Indian Institute of Technology Madras
Chennai, 600 036, INDIA
$^1$e-mail: jitumath@yahoo.co.in
$^2$e-mail: radharam@iitm.ac.in


Abstract.In this paper, the characterisation of multipliers for ${L^{1}({H^n})}\rightarrow L^{p}(H^n)$ is discussed, where $H^n$ denotes the Heisenberg group. This result is also extended to multipliers for the vector valued functions from $L^{1}(H^n,A)$ into $L^{p}(H^n,A)$, where $A$ is a commutative Banach algebra with a bounded approximate identity.

Received: November 28, 2006

AMS Subject Classification: 42B15, 43A22

Key Words and Phrases: Bochner integral, Heisenberg group, multiplier, unitary representation, vector valued function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 4