Dellacherie investigated the convex Φ-extension of Doob’s inequality and obtained ||f*||≤qφ’||f||φ, positive submartingales f=（ft）t≥0, where Φ is an increasing convex function satisfying Φ（0）=0, （?）Φ（...Dellacherie investigated the convex Φ-extension of Doob’s inequality and obtained ||f*||≤qφ’||f||φ, positive submartingales f=（ft）t≥0, where Φ is an increasing convex function satisfying Φ（0）=0, （?）Φ（u）/u=∞ (such a function is展开更多
In this paper, we give a kind of T(b) Theorem on product domains. Roughly speaking, let T be a singular integral operator on R^(d_1)×R^(d_2), let T`t be T's transpose with respect to (x, u), or (y, v) or both...In this paper, we give a kind of T(b) Theorem on product domains. Roughly speaking, let T be a singular integral operator on R^(d_1)×R^(d_2), let T`t be T's transpose with respect to (x, u), or (y, v) or both, and let'T^(t(j)) he Tt's restriction on R^(dj), j=1, 2. Then T's L^2-boundedness follows from: T has WBP, and T^(t(j))(b_j)=0, where b_j is any pseudoaccretive function on R^(dj), j=1, 2.展开更多
After C. Fefferman and D. H. Phong, a series of papers have been devoted to the weighted Sobolev inequality and eigenvalue estimates of the Schrdinger operator. In this note, we consider the two-weight Sobolev inequal...After C. Fefferman and D. H. Phong, a series of papers have been devoted to the weighted Sobolev inequality and eigenvalue estimates of the Schrdinger operator. In this note, we consider the two-weight Sobolev inequality and want to know under what conditions we have for 1【p【q【∞,展开更多
The aim of this paper is establishing some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces. In particular, ...The aim of this paper is establishing some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces. In particular, the Φ-function nequalitities of sharp operators f_p~#, f_p~#, p-variation operators W_p, W_p and the martingale tranform operator T_v are discussed. It is proved that the boundedness of these operators characterizes the smoothness, convexity and UMD-property of Banach spaces.展开更多
文摘Dellacherie investigated the convex Φ-extension of Doob’s inequality and obtained ||f*||≤qφ’||f||φ, positive submartingales f=（ft）t≥0, where Φ is an increasing convex function satisfying Φ（0）=0, （?）Φ（u）/u=∞ (such a function is
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, we give a kind of T(b) Theorem on product domains. Roughly speaking, let T be a singular integral operator on R^(d_1)×R^(d_2), let T`t be T's transpose with respect to (x, u), or (y, v) or both, and let'T^(t(j)) he Tt's restriction on R^(dj), j=1, 2. Then T's L^2-boundedness follows from: T has WBP, and T^(t(j))(b_j)=0, where b_j is any pseudoaccretive function on R^(dj), j=1, 2.
基金Project supported by the National Natural Science Foundation of China
文摘After C. Fefferman and D. H. Phong, a series of papers have been devoted to the weighted Sobolev inequality and eigenvalue estimates of the Schrdinger operator. In this note, we consider the two-weight Sobolev inequality and want to know under what conditions we have for 1【p【q【∞,
文摘The aim of this paper is establishing some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces. In particular, the Φ-function nequalitities of sharp operators f_p~#, f_p~#, p-variation operators W_p, W_p and the martingale tranform operator T_v are discussed. It is proved that the boundedness of these operators characterizes the smoothness, convexity and UMD-property of Banach spaces.
