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.
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 2Ämneskategorier (SSIF 2025)
Matematisk analys
DOI
10.1142/S0219199719500664