In the Euclidean space, it is known that a function f in L^2 of a ball B, with vanishing average, is the divergence of a vector field F in L^ 2 and the L^2-norm of F in the ball B is controlled by the L^2-norm of f in the same ball B (times a constant ). In this note, we prove a similar result in any Carnot group G for a vanishing average f in L^p, when 1\le p < Q, where Q is the so-called homogeneous dimension of G.
Baldi, A., Franchi, B., Pansu, P. (In stampa/Attività in corso). Primitives of volume forms in Carnot groups. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, published online first, 1-21 [10.4171/rlm/1052].
Primitives of volume forms in Carnot groups
Baldi, Annalisa;Franchi, Bruno
;Pansu, Pierre
In corso di stampa
Abstract
In the Euclidean space, it is known that a function f in L^2 of a ball B, with vanishing average, is the divergence of a vector field F in L^ 2 and the L^2-norm of F in the ball B is controlled by the L^2-norm of f in the same ball B (times a constant ). In this note, we prove a similar result in any Carnot group G for a vanishing average f in L^p, when 1\le p < Q, where Q is the so-called homogeneous dimension of G.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
