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
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.