Good λ inequalities for the area integral and the nontangential maximal function
نویسندگان
چکیده
منابع مشابه
A Simple Proof of an Inequality Dominating the Area Integral by the Nontangential Maximal Function
As we know, this inequality is very important in Hp-theory, it is also a main difficulty in generalizing Hp-theory of one parameter to Hp -theory of several parameters, see [2, 6, 7, 8]. The first proof of (1) is probabilistic which was given by Burkholder, Gundy and Silverstein, see [1]; Fefferman and Stein first got an analytic proof of (1) by dealing with a kind of Green’s formula on R = ∪x∈...
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p A v = u , (1) holds for t = ) t ( = ) t ( , but not if 1 = p . Also for each < p 1 there exists a pair p A ) v , u ( so that (1) fails in the special case t = ) t ( = ) t ( [3, p. 395]. In these exceptional cases we have a weak type inequality. An excellent reference is the book by J.Garcia-Cuerva and J.L.Rubio de Francia [3]. We refer the reader interested in the current stat...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1986
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-83-3-251-262