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van Neerven, J.M.A.M. (author), Portal, Pierre (author), Sharma, Himani (author)We consider operators acting on a UMD Banach lattice X that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator (Formula Presented) acting on L<sup>2</sup>(R<sup>d</sup>). More precisely, we consider abstract harmonic oscillators of the form (Formula Presented) for tuples of...journal article 2023
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Lorist, E. (author), Nieraeth, Zoe (author)We prove that scalarvalued sparse domination of a multilinear operator implies vectorvalued sparse domination for tuples of quasiBanach function spaces, for which we introduce a multilinear analogue of the UMD condition. This condition is characterized by the boundedness of the multisublinear HardyLittlewood maximal operator and goes...journal article 2022
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Lorist, E. (author)In this dissertation we develop vectorvalued harmonic analysis methods. Particular emphasis is put on the study of stochastic singular integral operators, which arise naturally in the study of SPDE.doctoral thesis 2021
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Nieraeth, Z. (author)The subject of this thesis is the study of the multilinear Muckenhoupt weight classes and the quantitative boundedness of operators with respect to these weights in both the scalarvalued and the vectorvalued setting. This includes the study of multisublinear HardyLittlewood maximal operators, sparse forms, and multilinear Rubio de Francia...doctoral thesis 2021
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Yaroslavtsev, I.S. (author)This paper is devoted to tangent martingales in Banach spaces. We provide the definition of tangency through local characteristics, basic L<sup>p</sup> and øestimates, a precise construction of a decoupled tangent martingale, new estimates for vectorvalued stochastic integrals, and several other claims concerning tangent martingales and...journal article 2020
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van Neerven, J.M.A.M. (author), Portal, Pierre (author)We generalise the classical Weyl pseudodifferential calculus on R<sup>d</sup> to the setting of two dtuples of operators A = (A<sub>1</sub>,..., A<sub>d</sub>) and B = (B<sub>1</sub>,..., B<sub>d</sub>) acting on a Banach space generating bounded C0groups satisfying the Weyl canonical commutation relations. We show that the resulting Weyl...journal article 2020
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Yaroslavtsev, I.S. (author)In this thesis we study martingales and stochastic integration of processes with<br/>values in UMD Banach spaces.doctoral thesis 2019
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Veraar, M.C. (author), Yaroslavtsev, I.S. (author)In this paper we consider local martingales with values in a UMD Banach function space. We prove that such martingales have a version which is a martingale field. Moreover, a new Burkholder–Davis–Gundy type inequality is obtained.book chapter 2019
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Amenta, Alex (author), Lorist, E. (author), Veraar, M.C. (author)We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove LittlewoodPaleyRubio de Franciatype estimates and boundedness of variational Carleson operators for Banach function spaces with UMD concavifications.journal article 2019
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Lorist, E. (author), Nieraeth, Z. (author)We give an extension of Rubio de Francia’s extrapolation theorem for functions taking values in UMD Banach function spaces to the multilinear limited range setting. In particular we show how boundedness of an m(sub)linear operator T:Lp1(w1p1)×⋯×Lpm(wmpm)→Lp(wp) for a certain class of Muckenhoupt weights yields an extension of the operator...journal article 2019
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Yaroslavtsev, I.S. (author)In this paper, we consider Meyer–Yoeurp decompositions for UMD Banach spacevalued martingales. Namely, we prove that X is a UMD Banach space if and only if for any fixed p ∈ (1, ∞), any Xvalued L<sup>p</sup>martingale M has a unique decomposition M = M<sup>d</sup> + M<sup>c</sup> such that M<sup>d</sup> is a purely discontinuous martingale...journal article 2019
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Lindemulder, N. (author), Veraar, M.C. (author), Yaroslavtsev, I.S. (author)In this paper we show that Musielak–Orlicz spaces are UMD spaces under the socalled Δ<sub>2</sub> condition on the generalized Young function and its complemented function. We also prove that if the measure space is divisible, then a Musielak–Orlicz space has the UMD property if and only if it is reflexive. As a consequence we show that...book chapter 2019
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Lü, Qi (author), van Neerven, J.M.A.M. (author)Extending results of Pardoux–Peng and Hu–Peng, we prove wellposedness results for backward stochastic evolution equations in UMD Banach spaces.book chapter 2019
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Lorist, E. (author)We prove the ℓ<sup>s</sup>boundedness of a family of integral operators with an operatorvalued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the ℓ<sup>s</sup>boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a...book chapter 2019
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Yaroslavtsev, I.S. (author)In this paper we show sharp lower bounds for norms of even homogeneous Fourier multipliers in L(L<sup>p</sup>(R<sup>d</sup>;X)) for 1<p<∞and for a UMD Banach space X in terms of the range of the corresponding symbol. For example, if the range contains a<sub>1</sub>,…,a<sub>N</sub>∈C, then the norm of the multiplier exceeds ‖a<sub>1</sub...journal article 2018
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Lindemulder, N. (author), Meyries, Martin (author), Veraar, M.C. (author)We prove results on complex interpolation of vectorvalued Sobolev spaces over the halfline with Dirichlet boundary condition. Motivated by applications in evolution equations, the results are presented for Banach spacevalued Sobolev spaces with a power weight. The proof is based on recent results on pointwise multipliers in Bessel...journal article 2018
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Yaroslavtsev, I.S. (author)We introduce the notion of weak differential subordination for martingales, and show that a Banach space X is UMD if and only if for all p ∈ (1, ∞) and all purely discontinuous Xvalued martingales M and N such that N is weakly differentially subordinated to M, one has the estimate E  N<sub>∞</sub> <sup>p</sup> ≤ C<sub>p</sub>E M<sub>∞<...journal article 2018
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Veraar, M.C. (author), Yaroslavtsev, I.S. (author)In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous local martingales has such a quadratic variation. For this new class of cylindrical continuous local martingales we develop a stochastic integration...journal article 2016
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Pronk, M. (author)In this thesis we study stochastic evolution equations in Banach spaces. We restrict ourselves to the two following cases. First, we consider equations in which the drift is a closed linear operator that depends on time and is random. Such equations occur as mathematical models in for instance mathematical finance and filtration theory. Second,...doctoral thesis 2013
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 Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author) journal article 2008
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