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

ORCiD: ORCID iD icon https://orcid.org/0000-0003-1120-8707

Google scholar: Marco Fraccaroli

arXiv: Marco Fraccaroli

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.
in J. Fourier Anal. Appl. 27, 67 (2021). https://doi.org/10.1007/s00041-021-09869-4
arXiv preprint: https://arxiv.org/abs/2001.05903

Duality for double iterated outer L^p spaces.
arXiv preprint: https://arxiv.org/abs/2104.09472
Submitted, April 2021.

Uniform Fourier restriction for convex curves in ℝ².
arXiv preprint: https://arxiv.org/abs/2111.06874
Submitted, November 2021.

A uniform phase-plane projection. (with Olli Saari, Christoph Thiele)
In preparation.

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