scnews: "Asia-Pacific Analysis and PDE Seminar: Adam Sikora -- Square functions and Riesz transforms on a class of non-doubling manifolds" by Daniel Hauer

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

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Webinar Speaker

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.

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