CONICAL SQUARE FUNCTIONS AND NON-TANGENTIAL MAXIMAL FUNCTIONS WITH RESPECT TO THE GAUSSIAN MEASURE

被引:16
|
作者
Maas, Jan [1 ]
van Neerven, Jan [2 ]
Portal, Pierre [3 ]
机构
[1] Univ Bonn, Inst Appl Math, D-53115 Bonn, Germany
[2] Delft Univ Technol, Delft Inst Appl Math, NL-2600 GA Delft, Netherlands
[3] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France
关键词
Hardy spaces; Gaussian measure; Ornstein-Uhlenbeck operator; square function; maximal function; HARDY-SPACES; OPERATORS; BMO;
D O I
10.5565/PUBLMAT_55211_03
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study, in L(1) (R(n); gamma) with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in L(1)-norm by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda.
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页码:313 / 341
页数:29
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