Date of Award
5-1-2024
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
College/School/Department
Department of Mathematics and Statistics
Dissertation/Thesis Chair
Karin Reinhold
Committee Members
Steven Plotnick, Joshua Isralowitz, Martin Hildebrand
Subject Categories
Physical Sciences and Mathematics
Abstract
Let Y be a Banach space. An operator T ∈ L(Y) is a Ritt operator providedsupn n∥Tn − Tn+1∥ < ∞. For Ritt operators T in Lp, where 1 < p < ∞, the square function (?n2m+1|Tn(I − T)m+1f|2)1/2 is bounded. We show that (?nα|Tn(I − nn T)lf|s)1/s is bounded in L1 for for l > 0 and sl > α+1 and (?nα|Tn(I−Tl)f|s)1/s is n 1 + ?n n+1s1/s boundedinL forl∈Z ands>α+1.Wealsoconsider( nl|T lf−T l f|) l where {nl} is an increasing sequence with increasing gaps. Finally, we investigate the related variational and oscillation norms.
Recommended Citation
Hults, Jennifer M., "Square Functions For Ritt Operators In L1" (2024). Legacy Theses & Dissertations (2009 - 2024). 3324.
https://scholarsarchive.library.albany.edu/legacy-etd/3324
