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Title: Polar and AC operators, the Hilbert transform, and matrix-weighted shifts
Author: Wilson, Julie
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1997
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Well-bounded operators of type (B) are the building blocks for trigonometrically well-bounded, polar and AC operators. We examine the relationship between polar and AC operators of type (B) and explore the concepts of bounded variation and absolute continuity for functions defined on annuli. In 1973, Hunt, Muckenhoupt and Wheeden showed that the Hilbert transform is a bounded operator on a weighted Lp space precisely when the weight satisfies the Ap condition. This result is proved independently for Lp spaces over the reals, the circle and the integers. We investigate the inter-relationships between these three theorems and show that the theorems for the reals and the integers are equivalent.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available