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

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

Lorist, E.

Veraar, M.C. (mentor)

Electrical Engineering, Mathematics and Computer Science

Delft Institute of Applied Mathematics

Analysis

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setting for a large class of Banach function spaces X. For this we first extensively study the first part of an unpublished manuscript on the factorization of ℓ2-boundedness.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.

Maximal function
Hardy-Littlewood
Vector valued
Factorization
Integral operators
Maximal regularity

http://resolver.tudelft.nl/uuid:e9be1c62-0826-451b-a1f7-ec121d10e562

Student theses

master thesis

(c) 2016 Lorist, E.