Category: Harmonic Analysis
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Twisted Geometry and Discrete Foundations: Building Haar Bases for Quotient Structures
There is a particular satisfaction in finishing a paper that builds something from scratch. Not a refinement, not a generalization in the usual sense, but an actual construction, objects that didn’t exist before, assembled carefully from the ground up. Our recent work on Haar bases for multi-parameter twisted structures gave me that feeling, and it…
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Commutators and Paraproducts in Nonhomogeneous Settings: Some Recent Progress
Notes on our recent work extending sparse domination and characterizing dyadic Hilbert transform commutators Background and Motivation Our recent paper addresses some long standing questions about commutators and paraproducts when the underlying measure lacks the doubling property. This is an area where classical intuition often fails, making it both challenging and interesting to work in.…