Type: Seminar

Modified: Sun 20 Jun 2021 1616

Distribution: World

Expiry: 21 Jun 2021

CalTitle1: Square functions and Riesz transforms on a class of non-doubling manifolds

Auth: dhauer@73.70.50.210.sta.wbroadband.net.au (dhauer) in SMS-SAML

Dear friends and colleagues,

on **Monday, 21 June 2021 **at** 4 PM**,
** Associate Professor Adam Sikora ** (Macquarie University, Sydney, Australia) is giving a talk in our
Asia-Pacific Analysis and PDE Seminar on

**
Square functions and Riesz transforms on a class of non-doubling manifolds
**.

**Abstract:**

We consider a class of manifolds \(\mathcal{M}\) obtained by taking the connected sum of a finite number of \(N\)-dimensional Riemannian manifolds of the form \((\mathbb{R}^{n_i}, \delta) \times (\mathcal{M}_i, g)\), where \(\mathcal{M}_i\) is a compact manifold, with the product metric. The case of greatest interest is when the Euclidean dimensions \(n_i\) are not all equal. This means that the ends have different `asymptotic dimensions', and implies that the Riemannian manifold \(\mathcal{M}\) is not a doubling space. We completely describe the range of exponents \(p\) for which the Riesz transform and vertical square function on \(\mathcal{M}\) are bounded operators on \(L^p(\mathcal{M})\).

The talk is based on joint works with Andrew Hassell, Daniel Nix, and Julian Bailey.

More information and how to attend this talk can be found at the seminar webpage .

Best wishes,

Daniel

------

Adam Sikora

Associate Professor @ Macquarie University, Sydney.

Adam Sikora obtained his PhD from the Polish Academy of Science in 1994.
Between 1995 and 2001 he was a visiting fellow at the Australian National University.
Then he worked as Assistant Professor @ New Mexico State University (United States)
before joining Macquarie University in 2009.