Abstract. The following deals with the T (b) theorems of David, Journé, and Semmes [7] considered in a dyadic setting. We find sharp growth estimates for a global and a local dyadic T (b) Theorem. We use multiscale analysis and Haar wavelets in the local case.
in Oregon. As part of her role, she provides professional development to calculus faculty, oversees the training of undergraduate math tutors, and teaches in the math department. Her primary research interests include STEM faculty adoption of evidence-based practices, the relationship between instructor beliefs and practice, and institutional change of teaching cultures.
Given a function b, and using adapted Haar wavelets, we define a BMO-type norm which is dependent on b. In both global and local cases, we find the dependence of the bounds on f BMO by the bounds on the b-weighted BMO norm of f . We show that the dependence is sharp in the global case. Multiscale analysis is used in the local case. We formulate as corollaries global and local dyadic T (b) theorems whose hypotheses include a bound on the b-weighted BMO-norm of T * (1).
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