UPPER BEURLING DENSITY OF SYSTEMS FORMED BY TRANSLATES OF FINITE SETS OF ELEMENTS IN L p (R d )
UPPER BEURLING DENSITY OF SYSTEMS FORMED BY TRANSLATES OF FINITE SETS OF ELEMENTS IN L p (R d )
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DOI：
10.15352/bjma/1342210162
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发表时间：
2012-03
影响因子：
1.2
通讯作者：
Bei Liu;Rui Liu
中科院分区：
文献类型：
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作者：
Bei Liu;Rui Liu
本文证明了：如果有限不交的平移并Sn k = 1 {fk（x-）} ∈ k在Lp（Rd）中（1 <p <∞）是p '-Bessel序列，则不交并= Sn = 1k有有限的上Beurling密度，且若Sn = 1 {fk（x-）} ∈ k是1/p +1/q = 1的（Cq）-系，则具有无穷大的上Beurling密度。因此，对于任意1 <p '<∞，Lp（Rd）中平移的有限不交并集都不能构成p'-Bessel（Cq）-系.进一步，利用Banach空间几何的技巧，我们得到：当1 <p ≤ 2时，Lp（Rd）中平移的有限不交并不能形成无条件基.
In this paper, we prove that if a finite disjoint union of translates Sn k=1 {fk(x − )}∈ k in L p (R d ) (1 < p < ∞) is a p ' -Bessel sequence for some 1 < p ' < ∞, then the disjoint union = Sn=1 k has finite upper Beurling density, and that if Sn=1 {fk(x−)}∈ k is a (Cq)-system with 1/p+1/q = 1, then has infinite upper Beurling density. Thus, no finite disjoint unio n of translates in L p (R d ) can form a p ' -Bessel (Cq)-system for any 1 < p ' < ∞. Furthermore, by using techniques from the geometry of Banach spaces, we obtain that, for 1 < p ≤ 2, no finite disjoint union of translates in L p (R d ) can form an unconditional basis.