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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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Lorist, E. (author), Veraar, M.C. (author)We introduce CalderónZygmund theory for singular stochastic integrals with operatorvalued kernel. In particular, we prove L <sup>p</sup>extrapolation results under a Hörmander condition on the kernel. Sparse domination and sharp weighted bounds are obtained under a Dini condition on the kernel, leading to a stochastic version of the...journal article 2021
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Lorist, E. (author)We prove a general sparse domination theorem in a space of homogeneous type, in which a vectorvalued operator is controlled pointwise by a positive, local expression called a sparse operator. We use the structure of the operator to get sparse domination in which the usual ℓ<sup>1</sup>sum in the sparse operator is replaced by an ℓ<sup>r<...journal article 2020
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Hänninen, Timo S. (author), Lorist, E. (author)We study the domination of the lattice Hardy–Littlewood maximal operator by sparse operators in the setting of general Banach lattices. We prove that the admissible exponents of the dominating sparse operator are determined by the qconvexity of the Banach lattice.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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Frey, D. (author), Nieraeth, Z. (author)We consider operators T satisfying a sparse domination property (Formula presented.)with averaging exponents (Formula presented.). We prove weighted strong type boundedness for (Formula presented.) and use new techniques to prove weighted weak type (Formula presented.) boundedness with quantitative mixed (Formula presented.)–(Formula...journal article 2018