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On The P-Inner Functions Of ℓPA, James G. Dragas

Mathematics & Statistics Theses & Dissertations

Define ℓ^p_A as the space of all functions holomorphic over the unit disk whose Taylor coefficients are p-summable. Despite their classical origins and simple definition, these spaces are not as well understood as one might expect. This is particularly true when compared with the Hardy spaces, which provide a useful road map for the types of questions we might consider reasonable. In this work we examine the zero sets of ℓ^p_A, p ∈ (1;∞), as well as a notion of inner function that is consistent with the approach taken on numerous other function spaces. …