L¹-estimates for constant rank operators

2018/11/25 by Raiţă, Bogdan
#26D10 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.10057

Abstract

We show that the inequality ‖D^k-1(u-πu)‖_{L^n/(n-1)(ℝⁿ)}≤ c‖\mathbbB(D) u‖_L¹(ℝⁿ) holds for vector fields u\inC^∞_c if and only if \mathbbB is canceling. Here π denotes the L²-orthogonal projection onto the kernel of the k-homogeneous differential operator \mathbbB(D) of constant rank on ℝⁿ. Other critical embeddings are established.

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