## University COVID-19 update

### Questions about buildings and services? Visit the list of Modified Services.

Please note: The University of Waterloo is closed for all events until further notice.

# Analysis Seminar

Thursday, February 7, 2019 — 4:00 PM EST

[Talk rescheduled from February 6, 2019]

Sang-Gyun Youn, Queen's University

"Sobolev embedding properties on compact matrix quantum groups"

One of the equivalent statements of the fractional Sobolev embedding theorem on $\mathbb{T}^d$ with respect to the Laplacian operator $\Delta$ is that
$\left\|(1-\Delta)^{-\frac{d}{2}(\frac{1}{p}-\frac{1}{q})}\right\|_{L^q(\mathbb{T}^d)}\lesssim \| f \|_{L^p(\mathbb{T}^d)}$
for any $1<p<q<\infty$ and $f\in L^p(\mathbb{T}^d)$. The above inequality will be discussed within the category of compact quantum groups and main targets are compact Lie groups, duals of discrete groups and free orthogonal quantum groups. One of the main aims of this talk is to explain the following sharp inequality
$\|T(\lambda(f))\|_{L^q(\mathcal{L}(\mathbb{F}_N))}\lesssim \|\lambda(f)\|_{L^p(\mathcal{L}(\mathbb{F}_N))}~(1<p<q<\infty)$
where $\lambda(f)\sim \displaystyle \sum_{x\in \mathbb{F}_N}f(x)\lambda_x\in L^p(\mathcal{L}(\mathbb{F}_N))$ and $T(\lambda(f))\sim \displaystyle \sum_{x\in \mathbb{F}_N}\frac{f(x)}{(1+|x|)^{3(\frac{1}{p}-\frac{1}{q})}}\lambda_x$.

MC 5417

### March 2020

S M T W T F S
1
5
7
8
12
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1
2
3
4
1. 2020 (67)
1. May (3)
2. March (16)
3. February (26)
4. January (22)
2. 2019 (199)
1. December (7)
2. November (26)
3. October (19)
4. September (13)
5. August (7)
6. July (12)
7. June (18)
8. May (22)
9. April (11)
10. March (25)
11. February (17)
12. January (22)
3. 2018 (219)
4. 2017 (281)
5. 2016 (335)
6. 2015 (209)
7. 2014 (235)
8. 2013 (251)
9. 2012 (135)