Some remarks on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si15.svg"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> embeddings in the subelliptic setting
نویسندگان
چکیده
In this paper we establish an optimal Lorentz estimate for the Riesz potential in L1 regime setting of a stratified group G: Let Q?2 be homogeneous dimension G and I? denote order ? on G. Then, every ??(0,Q), there exists constant C=C(?,Q)>0 such that (0.1)?I?f?LQ?(Q??),1(G)?C?XI1f?L1(G)for all f?Cc?(G) XI1f?L1(G), where X denotes horizontal gradient.
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ژورنال
عنوان ژورنال: Nonlinear Analysis-theory Methods & Applications
سال: 2021
ISSN: ['1873-5215', '0362-546X']
DOI: https://doi.org/10.1016/j.na.2020.112149