Journal of the Australian Mathematical Society (Series A)

Table of Contents - 1982 - Volume 33, Issue 02  

Research Article

Weyl functions and the Ap condition on compact lie groups

Giancarlo Travaglinia1

a1 Istituto Matematico dell'Università Via Saldini 50 20133 Milano, Italy

Abstract

Let G be a compact, simple, simply connected Lie group. The Lp-norm of a central trigonometric polynomial reduces naturally to a weighted Lp-norm of a trigonometric polynomial on a maximal torus T. The weight is | Δ |2-p, where Δ is the usual Weyl function. If p ≥ 2, we prove that | Δ |2-p satisfies Muckenhoupt's Ap condition if and only if the Lp-norms of the irreducible characters of G are uniformly bounded.

(Received February 26 1981)

(Revised August 11 1981)

1980 Mathematics subject classification (Amer. Math. Soc.)

  • primary 43 A 15, 22 E 30;
  • secondary 43 A 40