Given a monogenic function on the quaternionic algebra H, the Clifford algebra Rn or the octonionic algebra O we prove that | ∇ mf| α is subharmonic for some α> 0 where ∇ mf is the mth order gradient of f. We find also the optimal value of α. This is a generalization of a result of Calderon and Zygmund.
Higher Order Gradients of Monogenic Functions
Baracco L.
;
2022
Abstract
Given a monogenic function on the quaternionic algebra H, the Clifford algebra Rn or the octonionic algebra O we prove that | ∇ mf| α is subharmonic for some α> 0 where ∇ mf is the mth order gradient of f. We find also the optimal value of α. This is a generalization of a result of Calderon and Zygmund.
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