Joint BCAM-UPV/EHU Analysis and PDE seminar: Maximal operators on the infinite-dimensional toru

Date: Thu, Dec 16 2021

Hour: 17:00

Location: BCAM Seminar Room and Online

Speakers: Dariusz Kosz

LOCATION: BCAM Seminar Room and Online


We consider maximal operators MB associated with various differentiation bases B in the infinite-dimensional torus Tω. For the so-called Rubio de Francia basis R the operator MR is unbounded on Lp (Tω) for every p ∈ [1, ∞). On the other hand, the operator determined by the restricted (dyadic) basis R0 is of weak type (1, 1), hence bounded on Lp (Tω) for every p ∈ (1, ∞). We want to understand the interplay between the structure of B and the behavior of MB. For this purpose, we look for intermediate bases R0 ⊂ R ⊂ R which produce operators with more peculiar mapping properties. In particular, for any given p0 ∈ (1, ∞) we construct R such that MR is bounded on Lp (Tω) if and only if p ∈ (p0, ∞].

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Confirmed speakers:

Dariusz Kosz