Sharp Weak Type Inequality for Fractional Integral Operators Associated with d-Dimensional Walsh-Fourier Series

被引：4
作者：
Osekowski, Adam [1 ]
机构：
[1] Univ Warsaw, Dept Math Informat & Mech, PL-02097 Warsaw, Poland
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2014年 / 78卷 / 04期
关键词：
Fractional; best constant; weak-type inequality; Bellman function; MARCINKIEWICZ-FEJER MEANS; MAXIMAL OPERATOR; CESARO SUMMABILITY; BELLMAN FUNCTIONS; THEOREM;
D O I：
10.1007/s00020-013-2116-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Suppose that d >= 1 is an integer, is a fixed parameter and let I-alpha be the fractional integral operator associated with d-dimensional Walsh-Fourier series on [0, 1) (d) . The paper contains the proof of the sharp weak-type estimate parallel to I-alpha(f)parallel to L-d/(d-alpha),L- infinity([0,L-1)d) <= 2(d) - 1/(2(d-alpha) - 1)(2(alpha) - 1)parallel to f parallel to(L1([0,1)d)). The proof rests on Bellman-function-type method: the above estimate is deduced from the existence of a certain family of special functions.
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页码：589 / 600
页数：12
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