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.