Title: Boundedness of paraproduct operators on dyadic fractional Sobolev spaces

Abstract: We will characterize the boundedness of dyadic paraproducts on dyadic fractional Sobolev spaces, H^s, via a Carleson embedding theorem. As expected, the L^p-boundedness characterization via the dyadic BMO space is not sufficient in this setting. In order to encode the smoothness required in Sobolev spaces, we show that the correct spaces to characterize this boundedness are certain dyadic fractional BMO spaces, as it was first observed by Coifman and Murai for commutators in the continuous setting. We will also apply this result to prove the algebra property of the high-regularity Sobolev spaces and to establish the boundedness of the commutator with the Haar shift on H^s.

Short Bio: Valeria Fragkiadaki received her Ph.D. degree in Mathematics from Texas A&M University, in 2025, working under the supervision of Patricia Alonso Ruiz and Irina Holmes Fay. Before that she finished her Master's and Bachelor's degree at the University of Crete, in Greece. She is currently a Postdoctoral Fellow at Clemson University under the mentorship of Cody Stockdale and Mishko Mitkovski. Her research interests lie in harmonic analysis, with a focus on dyadic harmonic analysis: dyadic paraproducts, sparse operators, weighted inequalities and applications to Sobolev spaces.