WEAK TYPE (1,1) BEHAVIOR FOR THE LITTLEWOOD-PALEY g-FUNCTION

被引:1
作者
Lai, Xudong [1 ]
机构
[1] Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, Peoples R China
基金
中国国家自然科学基金; 中国博士后科学基金;
关键词
Littlewood-Paley g function; weak type (1,1) bounds; best constant; BOUNDS; CUBES;
D O I
10.4064/cm8854-5-2022
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For f is an element of L-p(R-n) (1 <= p < infinity), the classical Littlewood-Paley g-function is defined by g(f)(x) = (integral(infinity)(0) vertical bar del u(x, t)vertical bar(2)t dt)(1/2), where u(x, t) denotes the Poisson integral of f. The following two weak type (1, 1) behaviors for the operator g are established: lambda m({x is an element of R-n : g(f)(x) > lambda}) less than or similar to n(3)parallel to f parallel to(1), lim(lambda -> 0+) lambda m({x is an element of R-n : g(f)(x) > lambda}) = root 2 c(n)omega(n-1)/2n vertical bar integral(Rn) f(x) dx vertical bar, for any f is an element of L-1(R-n), where c(n) is the constant in the Poisson kernel and omega(n-1) is the area of the unit sphere in R-n.
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页码:285 / 302
页数:18
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