Maximal functions, factorization, and the R-boundedness of integral operators

Master thesis

Authors

Contributors

M.C. Veraar (mentor)
Programme
Analysis (EEMCS) (TU Delft)
Copyright: © 2016 Lorist, E.
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Programme

Analysis

Abstract

We generalize a recent result on the ℓs-boundedness of a family of integral operators from the weighted vector-valued Lp(Rd,w;Lq(Ω)) setting to the weighted vector-valued Lp(Rd,w;X) setting for a large class of Banach function spaces X. For this we first extensively study the first part of an unpublished manuscript on the factorization of ℓ2-boundedness. Afterwards we introduce some notions from harmonic analysis and study the behaviour of the Hardy-Littlewood maximal function in this weighted vector-valued setting through dyadic analysis. Finally we lift a result of Rubio de Francia on weighted versus vector-valued inequalities to this setting to conclude with the generalization of the result on the ℓs-boundedness of a family of integral operators.