TY - JOUR

T1 - Some remarks on L1 embeddings in the subelliptic setting

AU - Krantz, Steven G.

AU - Peloso, Marco M.

AU - Spector, Daniel

N1 - Funding Information:
The groundwork for this paper was laid while the second and third named authors were visiting the Department of Mathematics at Washington University in St. Louis. We wish to extend our gratitude to this institution for the hospitality and the pleasant and stimulating working environment provided. The authors would like to thank Gerald Folland for discussions regarding stratified groups and maximal function bounds in this setting. The second author is supported in part by the 2015 PRIN grant Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis. The third author is supported in part by the Taiwan Ministry of Science and Technology under research grants 107-2918-I-009-003 and 107-2115-M-009-002-MY2.
Funding Information:
The groundwork for this paper was laid while the second and third named authors were visiting the Department of Mathematics at Washington University in St. Louis. We wish to extend our gratitude to this institution for the hospitality and the pleasant and stimulating working environment provided. The authors would like to thank Gerald Folland for discussions regarding stratified groups and maximal function bounds in this setting. The second author is supported in part by the 2015 PRIN grant Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis. The third author is supported in part by the Taiwan Ministry of Science and Technology under research grants 107-2918-I-009-003 and 107-2115-M-009-002-MY2 .
Publisher Copyright:
© 2020 The Author(s)

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

UR - http://www.scopus.com/inward/record.url?scp=85091601742&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85091601742&partnerID=8YFLogxK

U2 - 10.1016/j.na.2020.112149

DO - 10.1016/j.na.2020.112149

M3 - Article

AN - SCOPUS:85091601742

VL - 202

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

M1 - 112149

ER -