UPPER BEURLING DENSITY OF SYSTEMS FORMED BY TRANSLATES OF FINITE SETS OF ELEMENTS IN L-P(R-d)

作者：Liu Bei; Liu Rui

来源：Banach Journal of Mathematical Analysis, 2012, 6(2): 86-97.

• (C-q)-system
• L-P-space
• p '
• -Bessel sequence
• translate
• upper Beurling density

In this paper, we prove that if a finite disjoint union of translates U-k=1(n) if {f(k) (X -gamma)}(gamma is an element of Gamma k) in L-P(R-d) (1 < p < infinity) is a p';-Bessel sequence for some 1 < p'; < infinity, then the disjoint union Gamma = U-k=1(n) Gamma(k) has finite upper Beurling density, and that if U-k=1(n) {f(k)(X -gamma)}(gamma is an element of Gamma k) (C-q)-system with 1/p + 1/q = 1, then F has infinite upper Beurling density. Thus, no finite disjoint union of translates in LP(I) can form a p';-Bessel (Cq)-system for any 1 < p'; < pc. 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.

• 出版日期2012
• 单位南开大学; 天津理工大学