Date of Graduation
7-2021
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
Daniel Luecking
Committee Member
John Akeroyd
Second Committee Member
Maria Tjani
Keywords
Bergman Space, Carleson Measures, Interpolation, Sampling, Tent Spaces
Abstract
Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in harmonic analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have been a recent focus of research. We introduce the concept of interpolating and sampling sequences for analytic tent spaces analogously to the same concepts for Bergman spaces. We then characterize such sequences in terms of Seip's upper and lower uniform density. We accomplish this by exploiting a kind of Mobius invariance for the tent spaces.
Citation
Parks, C. (2021). Interpolation and Sampling in Analytic Tent Spaces. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/4143
Included in
Analysis Commons, Harmonic Analysis and Representation Commons, Logic and Foundations Commons