Some remarks on L1 embeddings in the subelliptic setting

Steven G. Krantz; Marco M. Peloso; Daniel Spector

doi:10.1016/j.na.2020.112149

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

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

3 引文斯高帕斯（Scopus）

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 I_α 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 ‖I_αf‖_{L^{Q∕(Q−α),1}(G)}≤C‖XI₁f‖_L¹(G)for all f∈C_c^∞(G) such that XI₁f∈L¹(G), where X denotes the horizontal gradient.

原文	英語
文章編號	112149
期刊	Nonlinear Analysis, Theory, Methods and Applications
卷	202
DOIs	https://doi.org/10.1016/j.na.2020.112149
出版狀態	已發佈 - 2021 1月
對外發佈	是

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10.1016/j.na.2020.112149

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title = "Some remarks on L1 embeddings in the subelliptic setting",

abstract = "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.",

keywords = "L regime, Lorentz spaces, Sobolev embeddings, Stratified group, Subelliptic estimates",

author = "Krantz, {Steven G.} and Peloso, {Marco M.} and Daniel Spector",

note = "Publisher Copyright: {\textcopyright} 2020 The Author(s)",

year = "2021",

month = jan,

doi = "10.1016/j.na.2020.112149",

language = "English",

volume = "202",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

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T1 - Some remarks on L1 embeddings in the subelliptic setting

AU - Krantz, Steven G.

AU - Peloso, Marco M.

AU - Spector, Daniel

PY - 2021/1

Y1 - 2021/1

N2 - 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.

AB - 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.

KW - L regime

KW - Lorentz spaces

KW - Sobolev embeddings

KW - Stratified group

KW - Subelliptic estimates

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DO - 10.1016/j.na.2020.112149

M3 - Article

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SN - 0362-546X

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 112149

ER -

Some remarks on L1 embeddings in the subelliptic setting

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Some remarks on L¹ embeddings in the subelliptic setting