| Popis: |
In this paper, we prove that the product (in the distribution sense) of two functions, which are respectively in BMO ( R n ) and H 1 ( R n ) , may be written as the sum of two continuous bilinear operators, one from H 1 ( R n ) × BMO ( R n ) into L 1 ( R n ) , the other one from H 1 ( R n ) × BMO ( R n ) into a new kind of Hardy–Orlicz space denoted by H log ( R n ) . More precisely, the space H log ( R n ) is the set of distributions f whose grand maximal function M f satisfies ∫ R n | M f ( x ) | log ( e + | x | ) + log ( e + | M f ( x ) | ) d x ∞ . The two bilinear operators can be defined in terms of paraproduct. As a consequence, we find an endpoint estimate involving the space H log ( R n ) for the div-curl lemma. |
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