Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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[Talk rescheduled from February 6, 2019]
SangGyun 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
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Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca