In this paper the classical Besov spaces B^sp.q and Triebel-Lizorkin spaces F^sp.q for s∈R are generalized in an isotropy way with the smoothness weights { ｜2j｜^α→ln }7=0. These generalized Besov spaces and Trie...In this paper the classical Besov spaces B^sp.q and Triebel-Lizorkin spaces F^sp.q for s∈R are generalized in an isotropy way with the smoothness weights { ｜2j｜^α→ln }7=0. These generalized Besov spaces and Triebel-Lizorkin spaces, denoted by B^α→p.q and F^α→p.q for α^→ E Nk and k ∈N, respectively, keep many interesting properties, such as embedding theorems （with scales property for all smoothness weights）, lifting properties for all parameters 5, and duality for index 0 〈 p 〈∞ By constructing an example, it is shown that there are infinitely many generalized Besov spaces and generalized Triebel-Lizorkin spaces lying between B^sp.q and ∪t〉s B^tp.q, and between F^sp.q and ∪t〉s F^tp.q, respectively.展开更多
为 Gabor 的基本事实装裱 {E_(u (m) b )T_(u (n) 一) g )}_(m， n ∈ P ) 在本地人上，地被调查。精确地，正规框架双 {E_(u (m) b )T_(u (n) 一) g }_(m， n ∈ P ) 也， Gabor 结构被显示出；产品 ab 决定它是否是可能的为 {E_(u (m)...为 Gabor 的基本事实装裱 {E_(u (m) b )T_(u (n) 一) g )}_(m， n ∈ P ) 在本地人上，地被调查。精确地，正规框架双 {E_(u (m) b )T_(u (n) 一) g }_(m， n ∈ P ) 也， Gabor 结构被显示出；产品 ab 决定它是否是可能的为 {E_(u (m) b )T_(u (n) 一) g }_(m， n ∈ P ) 被讨论是为 L^2 (K) 的一个框架；一些必要条件和为 L^2 (K) 的 Gabor 框架的二个足够的条件被建立。一个例子最后被给。展开更多
基金Supported by NSFC of China under Grant #10571084NSC in Taipei under Grant NSC 94-2115-M-008-009(for the second author)
文摘In this paper the classical Besov spaces B^sp.q and Triebel-Lizorkin spaces F^sp.q for s∈R are generalized in an isotropy way with the smoothness weights { ｜2j｜^α→ln }7=0. These generalized Besov spaces and Triebel-Lizorkin spaces, denoted by B^α→p.q and F^α→p.q for α^→ E Nk and k ∈N, respectively, keep many interesting properties, such as embedding theorems （with scales property for all smoothness weights）, lifting properties for all parameters 5, and duality for index 0 〈 p 〈∞ By constructing an example, it is shown that there are infinitely many generalized Besov spaces and generalized Triebel-Lizorkin spaces lying between B^sp.q and ∪t〉s B^tp.q, and between F^sp.q and ∪t〉s F^tp.q, respectively.
基金Project supported by the National Natural Science Foundation of China (No. 10571084, No. 10671062) the Postdoctoral Science Foundation of China (No. 2005037694)the Natural Science Foundation of the Education Department of Henan Province of China (No. 2006110001).
文摘为 Gabor 的基本事实装裱 {E_(u (m) b )T_(u (n) 一) g )}_(m， n ∈ P ) 在本地人上，地被调查。精确地，正规框架双 {E_(u (m) b )T_(u (n) 一) g }_(m， n ∈ P ) 也， Gabor 结构被显示出；产品 ab 决定它是否是可能的为 {E_(u (m) b )T_(u (n) 一) g }_(m， n ∈ P ) 被讨论是为 L^2 (K) 的一个框架；一些必要条件和为 L^2 (K) 的 Gabor 框架的二个足够的条件被建立。一个例子最后被给。
