The Lp,q-stability of the Shifts of Finitely Many Functions in Mixed Lebesgue Spaces Lp,q(.d+1)

Authors
Li, Rui Liu, Bei Liu, Rui Zhang, Qing Yue
Citation
Li, Rui et al., The Lp,q-stability of the Shifts of Finitely Many Functions in Mixed Lebesgue Spaces Lp,q(.d+1), Acta mathematica Sinica. English series (Print) , 34(6), 2018, pp. 1001-1014
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
34
Issue
6
Year of publication
2018
Pages
1001 - 1014
Database
ACNP
SICI code
Abstract
The stability is an expected property for functions, which is widely considered in the study of approximation theory and wavelet analysis. In this paper, we consider the Lp,q-stability of the shifts of finitely many functions in mixed Lebesgue spaces Lp,q(.d+1). We first show that the shifts .(· . k) (k . .d+1) are Lp,q-stable if and only if for any . . .d+1, .k.Zd+1|.^(.+2.k)|2>0. Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces Lp,q(.d+1) to be Lp,q-stable which improves some known results.