ABSTRACT
Perhaps the most important idea for using Clifford algebras in harmonic analysis is to extend a function of n real variables monogenically (holomorphically if n = 1) to a function of n + 1 real variables with values in a complex Clifford algebra and to use the power of Clifford analysis and the associated function theory. A great amount of work has been done by many authors along these lines. We refer the reader to [GM], [LMcS] and [Mc] and references therein. In this paper, by using Clifford algebra, we get another two factorizations for functions in the Hardy space H 1 (ℝ n ). We find links between our results, the main result in [CRW] and the div- curl result about the compensated compactness in [CLMS], thereby giving different proofs to those results. Applications on the regularity of certain nonlinear quantities in PDE are also indicated.
