A trace theorem for Martinet-type vector fields
Artikel i vetenskaplig tidskrift, 2021

In R3ℝ3 we consider the vector fields

X1=∂∂x,X2=∂∂y+|x|α∂∂z,X1=∂∂x,X2=∂∂y+|x|α∂∂z,
where α∈[1,+∞[α∈1,+∞. Let R3+={(x,y,z)∈R3:z≥0}ℝ+3={(x,y,z)∈ℝ3:z≥0} be the (closed) upper half-space and let f∈C1(R3+)f∈C1(ℝ+3) be a function such that X1f,X2f∈Lp(R3+)X1f,X2f∈Lp(ℝ+3) for some p>1p>1. In this paper, we prove that the restriction of ff to the plane z=0z=0 belongs to a suitable Besov space that is defined using the Carnot–Carathéodory metric associated with X1X1 and X2X2 and the related perimeter measure.

Författare

Daniele Gerosa

Lunds universitet

Roberto Monti

Università di Padova

Daniele Morbidelli

Universita di Bologna

Communications in Contemporary Mathematics

0219-1997 (ISSN) 17936683 (eISSN)

Vol. 23 2

Ämneskategorier (SSIF 2025)

Matematisk analys

DOI

10.1142/S0219199719500664

Mer information

Senast uppdaterat

2025-05-15