Given a monogenic function on the quaternionic algebra H, the Clifford algebra Rn or the octonionic algebra O we prove that |del(m) f|(alpha) is subharmonic for some alpha > 0 where del m f is the mth order gradient of f. We find also the optimal value of alpha. This is a generalization of a result of Calderon and Zygmund.
Higher Order Gradients of Monogenic Functions
S. Pinton
2022-01-01
Abstract
Given a monogenic function on the quaternionic algebra H, the Clifford algebra Rn or the octonionic algebra O we prove that |del(m) f|(alpha) is subharmonic for some alpha > 0 where del m f is the mth order gradient of f. We find also the optimal value of alpha. This is a generalization of a result of Calderon and Zygmund.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
higher_gradient.pdf
Accesso riservato
:
Publisher’s version
Dimensione
388.89 kB
Formato
Adobe PDF
|
388.89 kB | Adobe PDF | Visualizza/Apri |
|
11311-1221433_Pinton.pdf
accesso aperto
:
Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione
254.31 kB
Formato
Adobe PDF
|
254.31 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
