Endpoint for the div-curl lemma in Hardy spaces

By A. Bonami, J. Feuto, Sandrine Grellier. 2008

64 citations recorded by the source corpus.

We give a div-curl type lemma for the wedge product of closed differential forms on Rn when they have coefficients respectively in a Hardy space and L∞ or BMO. In this latter case, the wedge product belongs to an appropriate Hardy-Orlicz space.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/030ca96a64b6bbfa5542def55f40ccdcf03954b7

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In Applied Mathematics

1. Dachun Yang
2. Yiyu Liang
3. Sibei Yang
4. Luong Dang Ky
5. Wen Yuan
6. Jizheng Huang
7. The Anh Bui
8. Jun Cao

In Mathematical Physics

1. Dachun Yang
2. Luong Dang Ky
3. Sibei Yang
4. Yiyu Liang
5. The Anh Bui
6. Wen Yuan
7. Jizheng Huang
8. Jun Cao

Citations in the corpus

• Musielak–Orlicz–Hardy Spaces Associated with Operators and Their Applications (2012, background): “Furthermore, some interesting applications of the spaces Hφ(R n) and BMOφ(R n) were given in [11, 13, 14, 63, 64, 65, 66].”
• Paraproducts and products of functions in BMO(Rn) and H1(Rn) through wavelets (2012, background): “To illustrate this phenomenon, it has been proven in [1] that, whenever F and G are two vector fields respectively in H1(Rn,Rn) and BMO(R,R) such that F is curl-free and G is div-free, then their scalar product F · G is in HΦ w(R,R) (in fact there is additional”
• New Hardy Spaces of Musielak–Orlicz Type and Boundedness of Sublinear Operators (2011, background): “A particular case of Hardy spaces of Musielak–Orlicz type appears naturally when considering the products of functions in BMO(R) and H(1)(R) (see [6]); and the endpoint estimates for the div-curl lemma (see [4,6]).”
• New real-variable characterizations of Musielak-Orlicz Hardy spaces (2012, background): “It is worth noticing that some special Musielak-Orlicz Hardy spaces appear naturally in the study of the products of functions in BMO(Rn) and H1(Rn) (see [7, 8]), and the endpoint estimates for the div-curl lemma and the commutators of singular integral operators (see [5, 7, 25]).”
• Musielak-Orlicz Campanato Spaces and Applications (2013, background): “It is also worth noticing that some special Musielak-Orlicz Hardy spaces appear naturally in the study of the products of functions in BMO(Rn) and H1(Rn) (see [5, 6]), and the endpoint estimates for the div-curl lemma and the commutators of singular integral operators (see [3, 5, 23]).”
• Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications (2012, background): “Furthermore, some interesting applications of these spaces were also presented in [4, 6, 7, 34, 35, 36].”
• Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates (2013, background): “Furthermore, Strömberg [68] and Janson [44] introduced the Orlicz-Hardy space which plays an important role in studying the theory of nonlinear PDEs (see, for example, [13, 14, 16, 36, 43]).”