# Some remarks on L1 embeddings in the subelliptic setting

Steven G. Krantz, Marco M. Peloso, Daniel Spector*

*此作品的通信作者

## 摘要

In this paper we establish an optimal Lorentz estimate for the Riesz potential in the L1 regime in the setting of a stratified group G: Let Q≥2 be the homogeneous dimension of G and Iα denote the Riesz potential of order α on G. Then, for every α∈(0,Q), there exists a constant C=C(α,Q)>0 such that ‖Iαf‖LQ∕(Q−α),1(G)≤C‖XI1f‖L1(G)for all f∈Cc(G) such that XI1f∈L1(G), where X denotes the horizontal gradient.

原文 英語 112149 Nonlinear Analysis, Theory, Methods and Applications 202 https://doi.org/10.1016/j.na.2020.112149 已發佈 - 2021 一月 是

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