Journal of Operator Theory

Volume 35, Issue 2, Spring 1996 pp. 349-372.

Conformal transformations and Hardy spaces arising in Clifford analysis

Authors: Tao Qian (1) and John Ryan (2)
Author institution:(1) Department of Mathematics, University of New England, Armidale, NSW 2351, AUSTRALIA
(2) Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, U.S.A.

Summary: Vahlen matrices are used to study the conformal covariance of various types of Hardy spaces over surfaces in euclidean space. These are Hilbert spaces associated to monogenic function spaces. Particular emphasis is made for the cases where the surfaces bound unbounded domains, particularly Lipschitz domains. An analogous study is made of Hardy type spaces over special types of surfaces lying in the conformal closure of $\mathbb C^n$.

Keywords: Hardy spaces over surfaces, monogenic function spaces, Lipschitz domains, Vahlen matrices, conformal covariance.

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