Title: Fractional Sobolev Embeddings and Algebra Property: A Dyadic View.

Abstract: In this talk, we revisit classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space $H^s(\mathbb{R})$ from a dyadic point of view. Inspired by previous work due to Aimar et al. we use Haar functions and dyadic decompositions to obtain the dyadic analogues of these classic results. Especially, in low regularities we provide explicit examples for the failure of the algebra property without using the Fourier transform.

About the Speaker: Valeria  Fragkiadaki received her PhD in 2025 from Texas A&M University  under the supervision of Irina Holmes-Fay and Patricia Alonso Ruiz. She received her BS and MS in Mathematics from the University of Crete, Greece. Currently she is a Postdoctoral Fellow at  Clemson University. Her research interests lie in the field of harmonic analysis focused mostly on dyadic harmonic analysis: dyadic paraproducts, sparse operators, weighted inequalities and applications to Sobolev spaces, she is also interested in harmonic analysis on the Hamming cube.  Valeria has two papers already published in Rev. Mat. Iberoamericana and Studia Mat., and she has several preprints already posted in the arXiv.