کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4644109 1341797 2012 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Paraproducts and products of functions in BMO(Rn)BMO(Rn) and H1(Rn)H1(Rn) through wavelets
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Paraproducts and products of functions in BMO(Rn)BMO(Rn) and H1(Rn)H1(Rn) through wavelets
چکیده انگلیسی

In this paper, we prove that the product (in the distribution sense) of two functions, which are respectively in BMO(Rn)BMO(Rn) and H1(Rn)H1(Rn), may be written as the sum of two continuous bilinear operators, one from H1(Rn)×BMO(Rn)H1(Rn)×BMO(Rn) into L1(Rn)L1(Rn), the other one from H1(Rn)×BMO(Rn)H1(Rn)×BMO(Rn) into a new kind of Hardy–Orlicz space denoted by Hlog(Rn)Hlog(Rn). More precisely, the space Hlog(Rn)Hlog(Rn) is the set of distributions f   whose grand maximal function MfMf satisfies∫Rn|Mf(x)|log(e+|x|)+log(e+|Mf(x)|)dx<∞. The two bilinear operators can be defined in terms of paraproduct. As a consequence, we find an endpoint estimate involving the space Hlog(Rn)Hlog(Rn) for the div-curl lemma.

RésuméDans cet article, on démontre que le produit, au sens des distributions, dʼune fonction BMO(Rn)BMO(Rn) et dʼune fonction H1(Rn)H1(Rn) peut sʼécrire comme somme dʼimages de deux opérateurs bilinéaires continus, lʼun de H1(Rn)×BMO(Rn)H1(Rn)×BMO(Rn) dans L1(Rn)L1(Rn), lʼautre de H1(Rn)×BMO(Rn)H1(Rn)×BMO(Rn) à valeurs dans un nouveau type dʼespace de Hardy, noté Hlog(Rn)Hlog(Rn). Plus précisément, lʼespace Hlog(Rn)Hlog(Rn) est lʼensemble des distributions f   dont la fonction grand-maximale MfMf satisfait∫Rn|Mf(x)|log(e+|x|)+log(e+|Mf(x)|)dx<∞. Les deux opérateurs bilinéaires peuvent se définir en termes de paraproduit. On utilise ce résultat pour obtenir un lemme de type div-rot sur H1(Rn)H1(Rn)-BMO(Rn)BMO(Rn).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal de Mathématiques Pures et Appliquées - Volume 97, Issue 3, March 2012, Pages 230–241
نویسندگان
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