 document

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
 document

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
 document

Bonnema, D.M. (author)In this thesis we study the boundedness of a generalization of the HardyLittlewood maximal operator, involving rearrangement invariant Banach function space and indices of the spaces.<br/> We first consider a classical proof of boundedness of the HardyLittlewood maximal operator on rearrangement invariant Banach function spaces. After...bachelor thesis 2020
 document

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
 document

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
 document

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