A trace theorem for Martinet-type vector fields
Journal article, 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.

Author

Daniele Gerosa

Lund University

Roberto Monti

University of Padua

Daniele Morbidelli

University of Bologna

Communications in Contemporary Mathematics

0219-1997 (ISSN) 17936683 (eISSN)

Vol. 23 2

Subject Categories (SSIF 2025)

Mathematical Analysis

DOI

10.1142/S0219199719500664

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Latest update

5/15/2025