Schur Multipliers of Divided Differences and Multilinear Harmonic Analysis

Master thesis (2024)

Authors

J. Reimann Electrical Engineering, Mathematics and Computer Science

Contributors

M.P.T. Caspers Analysis - EEMCS (supervisor 1)
F.M. de Oliveira Filho Discrete Mathematics and Optimization - EEMCS (supervisor 2)
S.E. Zegers Analysis - EEMCS (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: Ā© 2024 Jesse Reimann
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Published Date

01-02-2024

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

It was first shown by D. Potapov and F. Sukochev in 2009 that Lipschitz functions are also operator-Lipschitz on Schatten class operators Sp, 1
In this thesis, we offer an alternative boundedness proof for bilinear Schur multipliers of second order divided differences, in which we use recent results of multilinear harmonic analysis towards a multilinear transference proof, as well as recently found sufficient conditions for the boundedness of linear Schur multipliers which cannot be studied by transference. These methods were not known at the time Potapov, Skripka, and Sukochev proved their result.

Moreover, we show that this new proof improves the growth of the bound on the norm of the considered Schur multiplier for pā†’āˆž significantly. Finally, we give an outlook on further steps towards an alternative boundedness proof of multilinear Schur multipliers of divided differences of arbitrary order.