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Analysis Seminar – Brandon Sweeting
September 21, 2022 @ 11:00 am - 12:00 pm
Title: Mixed Weak-Type Estimates for Classical Operators
Abstract: We prove new mixed weak type estimates for various classical operators of Harmonic analysis. Mixed weak type inequalities were first studied by Muckenhoupt and Wheeden and later by Sawyer to prove the $L^p$ boundedness of the Hardy-Littlewood maximal operator as a consequence of the Jones factorization theorem. These inequalities are of interest given their connection to two weight inequalities and their use in defining a weighted weak-type space in the vector valued setting.
We obtain such estimates for the Hardy-Little maximal operator and Calderón–Zygmund operators using sparse domination techniques that generalize results of Cruz-Uribe, Isralowitz, Moen, Pott and Rivera-Ríos. We also do so for the fractional maximal operator and Riesz potentials, where we use an idea of Lacey, Moen, Pérez and Torres along with a generalization of an argument of Hedberg. This is joint work with David Cruz-Uribe.