We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob＇s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey sp...We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob＇s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob＇s inequality on martingale block spaces, we obtain the Davis＇ decompositions for martingale Morrey spaces.展开更多
In order to study the boundedness of some operators in general function spaces which include Lorentz spaces and Orlicz spaces as special examples,Lorentz introduced a new space called rearrangement invariant Banach fu...In order to study the boundedness of some operators in general function spaces which include Lorentz spaces and Orlicz spaces as special examples,Lorentz introduced a new space called rearrangement invariant Banach function spaces,denoted by RIBFS.It is shown in this paper that variation operators of singular integrals and their commutators are bounded on RIBFS whenever the kernels satisfy the L~r-H?rmander conditions.Moreover,we obtain some quantitative weighted bounds in the quasi-Banach spaces and modular inequalities for above variation operators and their commutators.展开更多
Assume that B is a separable real Banach space and X(t) is a diffusion process on B. In thispaper, we will establish the representation theorem of martingale additive functionals of X(t).
Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a r...Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t).展开更多
Let （Ω, ∑） be a measurable space and mo ： E→ Xo and m1 ： E → X1 be positive vector measures with values in the Banach KSthe function spaces Xo and X1. If 0 〈 a 〈 1, we define a X01-ax1a new vector measure [...Let （Ω, ∑） be a measurable space and mo ： E→ Xo and m1 ： E → X1 be positive vector measures with values in the Banach KSthe function spaces Xo and X1. If 0 〈 a 〈 1, we define a X01-ax1a new vector measure [m0, m]a with values in the Calderdn lattice interpolation space and we analyze the space of integrable functions with respect to measure [m0, m1]a in order to prove suitable extensions of the classical Stein Weiss formulas that hold for the complex interpolation of LP-spaces. Since each p-convex order continuous Kothe function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces.展开更多
基金The questions were posed during B. de Pagter was visiting the Queen's University of Belfast in Spring 1997, whilst the second author stayed at Belfast
文摘In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.
文摘We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob＇s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob＇s inequality on martingale block spaces, we obtain the Davis＇ decompositions for martingale Morrey spaces.
基金supported partly by the National Key R&D Program of China (Grant No.2020YFA0712900)NNSF of China (Grant Nos. 11871101, 12271041)。
文摘In order to study the boundedness of some operators in general function spaces which include Lorentz spaces and Orlicz spaces as special examples,Lorentz introduced a new space called rearrangement invariant Banach function spaces,denoted by RIBFS.It is shown in this paper that variation operators of singular integrals and their commutators are bounded on RIBFS whenever the kernels satisfy the L~r-H?rmander conditions.Moreover,we obtain some quantitative weighted bounds in the quasi-Banach spaces and modular inequalities for above variation operators and their commutators.
文摘Assume that B is a separable real Banach space and X(t) is a diffusion process on B. In thispaper, we will establish the representation theorem of martingale additive functionals of X(t).
基金This project is supported by the National Natural Science Foundation of China
文摘Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t).
文摘Let （Ω, ∑） be a measurable space and mo ： E→ Xo and m1 ： E → X1 be positive vector measures with values in the Banach KSthe function spaces Xo and X1. If 0 〈 a 〈 1, we define a X01-ax1a new vector measure [m0, m]a with values in the Calderdn lattice interpolation space and we analyze the space of integrable functions with respect to measure [m0, m1]a in order to prove suitable extensions of the classical Stein Weiss formulas that hold for the complex interpolation of LP-spaces. Since each p-convex order continuous Kothe function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces.
