Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated with magnetic Schr?dinger operators

doi:10.1007/s11464-015-0432-8

Frontiers of Mathematics in China

2015, Vol. 10

Issue (5): 1203-1232 https://doi.org/10.1007/s11464-015-0432-8

本期目录

Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated with magnetic Schr?dinger operators

Dachun YANG^1,^2,^*(

),Dongyong YANG^1,²

1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

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Abstract：

Let φ be a growth function, and let A:=-(?-ia)?(?-ia)+V be a magnetic Schr?dinger operator on L2(?n),n≥2, where α:=(α1,α2,?,αn)∈Lloc2(?n,?n) and 0≤V∈Lloc1(?n). We establish the equivalent characterizations of the Musielak-Orlicz-Hardy space HA,φ(?n), defined by the Lusin area function associated with {e-t2A}t>0, in terms of the Lusin area function associated with {e-tA}t>0, the radial maximal functions and the nontangential maximal functions associated with {e-t2A}t>0 and {e-tA}t>0, respectively. The boundedness of the Riesz transforms LkA-1/2,k∈{1,2,?,n}, from HA,φ(?n) to Lφ(?n) is also presented, where L_k is the closure of ??xk-iαk in L2(?n). These results are new even when φ(x,t):=ω(x)tp for all x∈?nand t ∈(0,+∞) with p ∈(0, 1] and ω∈A∞(?n) (the class of Muckenhoupt weights on ?n).

Key words： Magnetic Schr?dinger operator Musielak-Orlicz-Hardy space Lusin area function growth function maximal function Riesz transform

收稿日期: 2014-07-23 出版日期: 2015-06-24

Corresponding Author(s): Dachun YANG

引用本文:

. [J]. Frontiers of Mathematics in China, 2015, 10(5): 1203-1232.
Dachun YANG,Dongyong YANG. Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated with magnetic Schr?dinger operators. Front. Math. China, 2015, 10(5): 1203-1232.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-015-0432-8
https://academic.hep.com.cn/fmc/CN/Y2015/V10/I5/1203

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