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
Lanzani, L., Stein, E.M. (2005). A note on div curl inequalities. MATHEMATICAL RESEARCH LETTERS, 12(1), 57-61 [10.4310/MRL.2005.v12.n1.a6].
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, 393–426I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
