In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
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 L^p,q-stability of the shifts of finitely many ...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 L^p,q-stability of the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1）. We first show that the shifts Φ（·- k） （k∈Z^d＋1） are L^p,q-stable if and only if for any ξ ∈R^d＋1,∑κ∈Z^d＋1 ]｜Φ^^（ξ ＋ 2πκ）]^2 〉 0. Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1） to be L^p,q-stable which improves some known results.展开更多
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11371200,11401435,11601383and 11671214)Hundred Young Academia Leaders Program of Nankai University
文摘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 L^p,q-stability of the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1）. We first show that the shifts Φ（·- k） （k∈Z^d＋1） are L^p,q-stable if and only if for any ξ ∈R^d＋1,∑κ∈Z^d＋1 ]｜Φ^^（ξ ＋ 2πκ）]^2 〉 0. Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1） to be L^p,q-stable which improves some known results.
