Weighted Hardy spaces and commutator estimates

• Grant number: 24/14727-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2025
• End date: July 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Willian Hans Goes Corrêa
• Grantee: Ben Hur Eidt
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 23/06973-2 - Interpolation theory and geometry of Banach Spaces, AP.JP

Abstract

The theory of Muckenhoupt weights allows us to characterize when Calderón-Zygmund operators are bounded on weighted Lp spaces. A consequence of that theory is the celebrated Coifman-Rochberg-Weiss Commutator Theorem, which states that the commutator between a BMO function and a Calderón-Zygmund operator is always bounded on Lp (p strictly greater than 1 and finite). The objective of this project is to expand the relationship between weights and commutators to the theory of Hardy spaces Hp, studying particular operators that appear in formulations of the Riemann Hypothesis and the Invariant Subspace Problem. (AU)