J Austral Math Soc Ser A 56 pp403--414, 1994.

Mobius Covariance of Iterated Dirac Operators

Jaak Peetre and Tao Qian

Abstract

Using Fourier Transforms, we give a new proof of certain identities for the fundamental solutions of the iterated Dirac operators D^l = (åⁿ_i=1 e_i ¶/¶x_i)^l , l Î Z₊ and D^l = (¶/¶x₀ + D)^l. Based on the close relationship between the fundamental solutions and the conformal weights we then give a simple proof of B. Bojarski's results on the conformal covariance of D^l. We also prove a new conformal covariance result of D.

1991 AMS Subject Classification: 30G35

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Authors

Jaak Peetre

Institut Mittag-Leffler, Auravagen 17, S-182 62 Djursholm, Sweden.

and

Department of Mathematics, University of Stockholm, Box 6701, S-113 85 Stockholm, Sweden.

Tao Qian

Department of Mathematics, University of New England, Armidale 2351, Australia.