Let O（PτL be the oscillation of the Possion semigroup associated with the parabolic Hermite operator = t-△＋｜x｜2. We show that O（PτL） is bounded from LP （Rn＋1） into itself for 1 〈 p 〈 ∞, bounded from L1...Let O（PτL be the oscillation of the Possion semigroup associated with the parabolic Hermite operator = t-△＋｜x｜2. We show that O（PτL） is bounded from LP （Rn＋1） into itself for 1 〈 p 〈 ∞, bounded from L1（Rn＋l） into weak-L1（Rn＋1） and bounded from Lc∞（Rn＋1） into BMO（Rn＋1）. In the case p = ∞ we show that the range of the image of the operator O（PτL） is strictly smaller than the range of a general singular operator.展开更多
Let （M,τ） be a noncommutative probability space, （Mn）n≥l a sequence of von Neumann subalgebras of M and N a von Neumann subalgebra of M. We introduce the notions of It-approach and orthogonal approach for （Mn）...Let （M,τ） be a noncommutative probability space, （Mn）n≥l a sequence of von Neumann subalgebras of M and N a von Neumann subalgebra of M. We introduce the notions of It-approach and orthogonal approach for （Mn）n≥1 and prove that ε（x｜Mn）Lp→ε（x｜N） for any x ∈ Lp（M） （1 ≤ p 〈 ∞） if and only if （Mn）n≥1 τ-approaches and orthogonally approaches N.展开更多
基金supported by National Natural Science Foundation of China(11471251 and 11671308)
文摘Let O（PτL be the oscillation of the Possion semigroup associated with the parabolic Hermite operator = t-△＋｜x｜2. We show that O（PτL） is bounded from LP （Rn＋1） into itself for 1 〈 p 〈 ∞, bounded from L1（Rn＋l） into weak-L1（Rn＋1） and bounded from Lc∞（Rn＋1） into BMO（Rn＋1）. In the case p = ∞ we show that the range of the image of the operator O（PτL） is strictly smaller than the range of a general singular operator.
基金supported by National Natural Science Foundation of China(11271293,11471251)the Research Fund for the Doctoral Program of Higher Education of China(2014201020205)
文摘Let （M,τ） be a noncommutative probability space, （Mn）n≥l a sequence of von Neumann subalgebras of M and N a von Neumann subalgebra of M. We introduce the notions of It-approach and orthogonal approach for （Mn）n≥1 and prove that ε（x｜Mn）Lp→ε（x｜N） for any x ∈ Lp（M） （1 ≤ p 〈 ∞） if and only if （Mn）n≥1 τ-approaches and orthogonally approaches N.
