Scalar and Operator-Valued Fourier-Haar Multipliers

Hugh Wark (Aviva)

Tuesday 20th October, 2015 16:00-17:00 Maths 522

Abstract

The Haar basis is an example of a wavelet basis in Lp[0,1] for 1<=p<infinity. It is a classical result of Paley and Marcinkiewicz that for 1<p<infinity this basis is an unconditional basis for Lp[0,1]. This means that every bounded sequence is a multiplier of the Haar basis in Lp[0,1] for 1<p<infinity. However for p=1 the Haar basis is a conditional basis of L1[0,1] so there are bounded sequences which are not multipliers of this basis.

 

In this talk we will give several proofs giving a characterisation of the sequences which are multipliers of the Haar basis of L1[0,1] and consider operator and scalar valued Haar multipliers between vector and scalar valued Lp([0,1],X) and Lq([0,1],Y) for different 1<=p,q<=infinity and Banach spaces X and Y.

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