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Next seminar:
Next seminar:
29/04/26 - Federico Santagati - 5:30 p. m.
29/04/26 - Federico Santagati - 5:30 p. m.
(Politecnico di Torino)
(Politecnico di Torino)
Hardy–Littlewood Maximal Operators on Gromov Hyperbolic Spaces
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Abstract. Let (X, d) be a geodesic Gromov hyperbolic space and let μ be a positive measure on X. Assume that μ is locally doubling and that the measure of metric balls satisfies ca^r ≤ μ(B_r(x)) ≤ Cb^r for all r > 1, x ∈ X, for some 1 < a ≤ b < a^2. We prove that the centred Hardy–Littlewood maximal operator is of weak type (log_a b, log_a b), and that this exponent is optimal. The proof is based on a geometric approximation of hyperbolic spaces by suitable graphs, called spiderwebs, which are 1–quasi-isometric to the original space. We also discuss the behaviour of the uncentred maximal operator, showing that its boundedness properties differ drastically from the centred case. Moreover, we show that, by replacing balls with suitable subsets in the definition of the uncentred maximal operator, one can recover strong-type L^p bounds for all p > 1. Based on joint works with N. Chalmoukis, S. Meda, and E. Papageorgiou.
This series of seminars is addressed to an audience interested in Harmonic Analysis in the broadest possible sense. The seminars will not necessarily concern the latest research results; the speaker may also give a talk about open problems or a survey colloquium.
The conferences take place generally every two weeks on Wednesday at 5:30 p. m. (Rome time).
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Organizers:
Tommaso Bruno (Università di Genova)
Valentina Casarino (Università degli Studi di Padova)
Bianca Gariboldi (Università degli Studi di Bergamo)
Alessio Martini (Politecnico di Torino)
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