ICTP Mathematics Seminar "ANALYSIS DAY" - Wednesday, 17 September, from 11:00 to 16:00/HYBRID - VENUE: Luigi Stasi Seminar Room

[ICTP Math Section]

*_ANALYSIS DAY
_*

Wednesday, 17 September 2025

VENUE: Luigi Stasi Seminar Room

/PLEASE NOTE, THE ZOOM LINK TO JOIN THE SEMINAR WILL FOLLOW AFTERWARDS/
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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.

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13:30 - 14:30: *Julian Weigt* (ICTP)

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.

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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.

All are welcome to attend.

/https://indico.ictp.it/event/11174/


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Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

For to be free is not merely to cast off one's chains, but to live in a way
that respects and enhances the freedom of others. Nelson Mandela
<https://www.ictp.it/>