Abstract
We study the generalized Beltrami equation , where is the left Dirac operator in acting on functions in and with values in the complex Clifford algebra , is its conjugate, and is a -valued function with compact support, with vanishing mean oscillation, satisfying , where are the coordinates of in . Let be a weight function in . We prove that if belongs to the Muckenhoupt class with , that makes continuous the Riesz potential , then for every , there exists a solution of the equation above satisfying for every distributional partial derivative. If , we prove the same result for any .
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Notes
No potential conflict of interest was reported by the authors.