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Brief communications

On Multipliers on Compact Lie Groups

M. V. Ruzhansky^a, J. Wirth<sup>b

a</sup> Imperial College London, Department of Mathematics
^b University of Stuttgart

Abstract: In this note we announce $L^p$ multiplier theorems for invariant and noninvariant operators on compact Lie groups in the spirit of the well-known Hörmander–Mikhlin theorem on $\mathbb R^n$ and its versions on the torus $\mathbb T^n$. Applications to mapping properties of pseudo-differential operators on $L^p$-spaces and to a priori estimates for nonhypoelliptic operators are given.

Keywords: multiplier, pseudo-differential operator, Lie group.

UDC: 517.518.12

Received: 18.07.2011

DOI: 10.4213/faa3101

 English version: Functional Analysis and Its Applications, 2013, 47:1, 72–75

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