Jarod Hart

A new proof of the bilinear T(1) Theorem

A new simple proof of the bilinear T(1) Theorem in the spirit of the proof of Coifman-Meyer of the celebrated result of David and Journé in the linear case is presented. This new proof is obtained independent of the linear T(1) Theorem by combining recent bilinear square function bounds and a paraproduct construction.

Mastery-Based Testing in Undergraduate Mathematics Courses

Abstract Mastery-based testing is an assessment scheme that challenges students to provide complete solutions to problems derived from clear course concepts. Students are allowed multiple attempts to demonstrate mastery, which helps create a classroom environment where students value persistence toward thorough understanding. In this paper, we describe in detail the benefits and implementation of mastery-based testing in college mathematics courses. We also summarize student response data that show positive reactions to this testing method.

John-Nirenberg Inequalities and Weight Invariant BMO Spaces

This work explores new deep connections between John–Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of BMO-type spaces. The results are formulated in a very general framework in which BMO spaces are constructed using a base of sets, used also to define weights with respect to a non-negative measure (not necessarily doubling), and an appropriate oscillation functional. This includes as particular cases many different function spaces on geometric settings of interest. As a consequence, the weight invariance of several BMO and Triebel–Lizorkin spaces considered in the literature is proved. Most of the invariance results obtained under this unifying approach are new even in the most classical settings.