Marco Fraccaroli

RG Analysis and Partial Differential Equations

Archives of the Mathematisches Forschungsinstitut Oberwolfach

Contact

Postal address:
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
D - 53115 Bonn

Office:
Endenicher Allee 60, N2.008
Phone: +49 (0) 228 73-6888
E-mail: mfraccar (at) math.uni-bonn.de

I am currently a PhD student. My advisor is Prof. Dr. Christoph Thiele.
My CV.

Research interests

My main areas of interest are real and harmonic analysis.

My first main research interest lies in L^p theory for outer measure spaces. In particular, I am studying the duality properties of the single and double iterated outer L^p spaces.

My second main research interest lies in time-frequency analysis. In particular, I am studying boundedness properties of multilinear forms with symmetries given by modulations and matrix dilations.

Finally, I have studied the uniform restriction problem for convex planar curves, without any additional assumption on their smoothness.

Publications and preprints

Duality for outer L^p_μ(ℓ^r) spaces and relation to tent spaces.
arXiv preprint: https://arxiv.org/abs/2001.05903
Submitted, March 2020.

Duality for double iterated outer L^p spaces.
In preparation.

A note on triangle inequality for outer L^p_μ(ℓ^∞) spaces.
In preparation.

Boundedness of multilinear forms associated with determinantal multipliers. (with Gennady Uraltsev)
In preparation.

Uniform Fourier restriction for convex curves in ℝ².
In preparation.

Theses

My Master’s Degree was obtained from Universität Bonn, Germany, by March 1st, 2017, with a thesis on the topic of:
On distributions with GL₂(ℝ) dilation symmetry.
Advisor: Prof. Dr. Christoph Thiele.
In this thesis we give a complete classification of the tempered distributions homogeneous of a certain degree under the GL_n(ℝ) dilations for n=1 and n=2.

My Bachelor’s Degree was obtained from Università degli Studi di Padova, Italy, by September 26th, 2014, with a thesis on the topic of:
The Yamabe equation: analysis and solutions via the moving sphere method and the maximum principle (in Italian).
Advisor: Prof. Dr. Roberto Monti.