Local Hardy-Littlewood-Sobolev inequalities for canceling elliptic differential operators

In this work, we investigate the limit case p = 1 p=1 of the classical Stein-Weiss inequality for the Riesz potential. Our main result is a characterization of this inequality for a special class of vector fields associated to cocanceling operators introduced by Van Schaftingen [J. Eur. Math. Soc. (JEMS) 15 (2013), pp. 877–921]. As application, we recover and improve some fractional inequalities associated to vector fields.

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Local Hardy-Littlewood-Sobolev inequalities for canceling elliptic differential operators

Cited by 2 publications

References 10 publications

A Note on Lebesgue Solvability of Elliptic Homogeneous Linear Equations with Measure Data

A Note on Lebesgue Solvability of Elliptic Homogeneous Linear Equations with Measure Data

Stein-Weiss inequality in 𝐿¹ norm for vector fields

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