In this note, the authors obtain the following inequality: If q 6= 1, n−1, then there exists a constant A such that for any smooth q-form u with compact support in Rn one has kukLn/(n−1) ≤ A[kdukL1 + kd ∗ukL1 ]. For q = 1, the result is that kukLn/(n−1) ≤ A[kdukL1 + kd ∗ukH1 ], and for q = n − 1, the result is that kukLn/(n−1) ≤ A[kdukH1 + kd ∗ukL1 ], where H1 is the real Hardy space. These inequalities are generalizations of the classical Gagliardo-Nirenberg inequality (q = 0) and of the recent one (q = 1) obtained by J. Bourgain and H. R. Brezis [J. Amer. Math. Soc. 16 (2003), no. 2, 393–426

A note on div curl inequalities

Lanzani L.
;
2005

Abstract

In this note, the authors obtain the following inequality: If q 6= 1, n−1, then there exists a constant A such that for any smooth q-form u with compact support in Rn one has kukLn/(n−1) ≤ A[kdukL1 + kd ∗ukL1 ]. For q = 1, the result is that kukLn/(n−1) ≤ A[kdukL1 + kd ∗ukH1 ], and for q = n − 1, the result is that kukLn/(n−1) ≤ A[kdukH1 + kd ∗ukL1 ], where H1 is the real Hardy space. These inequalities are generalizations of the classical Gagliardo-Nirenberg inequality (q = 0) and of the recent one (q = 1) obtained by J. Bourgain and H. R. Brezis [J. Amer. Math. Soc. 16 (2003), no. 2, 393–426
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/873327
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