On Hardy and Hardy-Littlewood transforms in classes of functions with given majorant of modulus of continuity

被引：0
|
作者：
Volosivets, S. S. [1 ]
机构：
[1] Saratov NG Chernyshevskii State Univ, Dept Mech & Math, Astrakhanskaya St 83, Saratov 410028, Russia
来源：
ACTA SCIENTIARUM MATHEMATICARUM | 2009年 / 75卷 / 1-2期
关键词：
Hardy-Littlewood operator; generalized Lipschitz classes; real Hardy space; functions of vanishing mean oscillation; direct approximation theorem;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
From the works of D.V. Giang and F. Moricz (see [5]) and B. I. Golubov (see [7]) it follows that the Hardy-Littlewood operator B(f)(x) = x(-1) integral(x)(0) f(t) dt, x not equal 0, is bounded on BMO(R). We prove that B is also bounded on VMO(R) and that the generalized Lipschitz classes H-X(omega) (R) under additional conditions are invariant with respect to the operator B. A direct approximation theorem for VMO(R) is also obtained.
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页码：265 / 274
页数：10
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