Paraproducts in one and several parameters
نویسندگان
چکیده
منابع مشابه
Paraproducts in One and Several Parameters
For multiparameter bilinear paraproduct operators B we prove the estimate B : L × L 7→ L, 1 < p, q ≤ ∞. Here, 1/p+ 1/q = 1/r and special attention is paid to the case of 0 < r < 1. (Note that the families of multiparameter paraproducts are much richer than in the one parameter case.) These estimates are the essential step in the version of the multiparameter Coifman-Meyer theorem proved by C. M...
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Let Mb be the operator of pointwise multiplication by b, that is Mb f = bf . Set [A,B] = AB−BA. The Reisz potentials are the operators Rα f(x) = ∫ f(x− y) dy |y|α , 0 < α < 1. They map L 7→ L, for 1 − α + 1 q = 1 p , a fact we shall take for granted in this paper. A Theorem of Chanillo MR84j:42027 [6] states that one has the equivalence ‖[Mb,Rα]‖p→q ≃ ‖b‖BMO with the later norm being that of th...
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We prove that mutlilinear paraproducts are bounded from products of Lebesgue spaces L1 ×· · ·×Lm+1 to Lp,∞, when 1 ≤ p1, . . . , pm+1 <∞, 1/p1+· · ·+1/pm+1 = 1/p. We focus on the endpoint case when some indices pj are equal to 1, in particular we obtain the new endpoint estimate L× · · · ×L → L1/(m+1),∞. In memory of Nigel Kalton
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2007
ISSN: 0933-7741,1435-5337
DOI: 10.1515/forum.2007.013