A convolution type characterization for Lp - multipliers for the Heisenberg group. Issue 2 (2007)

• Record Type: Journal Article
• Authors: Radha Radha, R. R.; Vijayarajan Vijayarajan, A.K. A.K.
• Other Names: Maligranda Maligranda Lech Lech Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 5:Issue 2(2007)
• Page Start: 175
• Page End: 182
• Publication Date: 2007
• Subjects: Group Fourier Transform -- Heisenberg group -- Multiplier -- Pseudomeasure; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2007/701403
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : It is well known that if m is an L p - multiplier for the Fourier transform on ℝ n ( 1 < p < ∞ ), then there exists a pseudomeasure σ such that T m f = σ * f . A similar result is proved for the group Fourier transform on the Heisenberg group H n . Though this result is already known in generality for amenable groups, a simple proof is provided in this paper.