排序方式: 共有36条查询结果,搜索用时 15 毫秒
1.
Mark C. Veraar 《Proceedings of the American Mathematical Society》2007,135(5):1477-1486
In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.
2.
Let be an operator weight, i.e. a weight function taking values in the bounded linear operators on a Hilbert space . We prove that if the dyadic martingale transforms are uniformly bounded on for each dyadic grid in , then the Hilbert transform is bounded on as well, thus providing an analogue of Burkholder's theorem for operator-weighted -spaces. We also give a short new proof of Burkholder's theorem itself. Our proof is based on the decomposition of the Hilbert transform into ``dyadic shifts'.
3.
设(Ω,,P)是概率空间,B是Banach空间.本文引入了一类新的鞅型序列──(B值)拟终鞅型序列,并研究了它们的收敛性与Banach空间的Radon-Nikodym性,一致光滑性和UMD性的依赖关系. 相似文献
4.
Let X be a Banach space. We show that each m : ? \ {0} → L (X ) satisfying the Mikhlin condition supx ≠0(‖m (x )‖ + ‖xm ′(x )‖) < ∞ defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is isomorphic to a Hilbert space; each bounded measurable function m : ? → L (X ) having a uniformly bounded variation on dyadic intervals defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is a UMD space. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an arbitrary real-valued continuous local martingale. We give several characterizations of integrability and prove a version of the Itô isometry, the Burkholder–Davis–Gundy inequality, the Itô formula and the martingale representation theorem. 相似文献
6.
《Mathematische Nachrichten》2018,291(10):1470-1485
In this paper we study a class of second order coefficient operators differential equation with general (possibly non local) boundary conditions. We obtain new results extending those given in a previous paper 1 . Existence, uniqueness and optimal regularity of the strict solution are proved in UMD spaces, using the well‐known Dore–Venni theorem. 相似文献
7.
Tuomas Hytönen 《Journal of Functional Analysis》2008,254(3):675-726
Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X -valued functions on Rn. We characterize Kato's square root estimates and the H∞-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp space. To do so, we develop various vector-valued analogues of classical objects in Harmonic Analysis, including a maximal function for Bochner spaces. In the special case X=C, we get a new approach to the Lp theory of square roots of elliptic operators, as well as an Lp version of Carleson's inequality. 相似文献
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9.
BU Shangquan Department of Mathematical Sciences Tsinghua University Beijing China 《中国科学A辑(英文版)》2006,49(4):574-576
We give a simpler proof of a result on operator-valued Fourier multipliers on Lp([0,2π]d;X) using an induction argument based on a known result when d=1. 相似文献
10.
UMD Banach spaces and square functions associated with heat semigroups for Schrödinger,Hermite and Laguerre operators
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Jorge J. Betancor Alejandro J. Castro Juan C. Fariña Lourdes Rodríguez‐Mesa 《Mathematische Nachrichten》2016,289(4):410-435
In this paper we define square functions (also called Littlewood‐Paley‐Stein functions) associated with heat semigroups for Schrödinger and Laguerre operators acting on functions which take values in UMD Banach spaces. We extend classical (scalar) ‐boundedness properties for the square functions to our Banach valued setting by using γ‐radonifying operators. We also prove that these ‐boundedness properties of the square functions actually characterize the Banach spaces having the UMD property. 相似文献