Starts 17 Sep 2025 11:00
Ends 17 Sep 2025 16:00
Central European Time
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ANALYSIS DAY
HYBRID
Leonardo Building - Luigi Stasi Seminar Room
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https://zoom.us/j/94027397321
Meeting ID: 940 2739 7321
Passcode: 100110
11:00 - 12:00: Andrea Olivo (BCAM - Bilbao, Spain)
Title: Some new thoughts on weighted Gagliardo–Nirenberg–Sobolev inequality
Abstract: It is well known that the celebrated Gagliardo estimate can be viewed as an extension of the classical isoperimetric inequality, although the best constant was not obtained by Gagliardo. In this talk, we will explore some generalizations of this result involving weights, and we will discuss how it can be extended beyond smooth domains. We will also consider certain two-weighted Sobolev inequalities.
13:30 - 14:30: Julian Weigt (ICTP)
Title: Regularity of maximal functions in higher dimensions
Title: Regularity of maximal functions in higher dimensions
Abstract: The classical Hardy-Littlewood maximal function theorem states that the Hardy-Littlewood maximal operator is a bounded operator on L^p(R^d) if and only if 1 < p <= ∞. In 1997 Juha Kinnunen proved the corresponding result for the gradient of the maximal function, i.e. that the L^p(R^d)-norm of the gradient of the maximal function is controlled by the L^p(R^d)-norm of the gradient of the function if 1 < p <= ∞. However, he provides no counterexample in the endpoint, and so in 2004 Hajłasz and Onninen formally posed the question if the endpoint gradient bound also holds.
Many special cases, generalizations and variations of this problem have been explored, with partial success. The original question by Hajłasz and Onninen remains unanswered. We discuss recent progress in higher dimensions, based on the coarea formula, dyadic decompositions and the relative isoperimetric inequality. As a by-product we obtain a Vitali-type covering lemma for the boundary.
15:00 - 16:00: Lucas Oliveira (UFRGS - Brazil)
Title: Extending homeomorphisms of the real line to the upper half plane
Abstract: Consider the following question: is it possible to extend a quasisymmetric homeomorphism of the real line to a quasiconformal homeomorphism of upper-half plane such that the extension of a composition it is the composition of the extensions?
An answer to this question is already known in this precise situation, but there are cases where these problems still need an answer (positive or negative). In this talk I would like to present the result of recent collaborations that provides some advance in the specific case of bi-Lipschitz homeomorphisms.
Joint work with José Afonso Barrionuevo, Felipe Gonçalves and Victor Medeiros.