Work

Square functions and variational estimates for Ritt operators on L 1 $L^1$ upper L Superscript 1

Year: 2026

Type: article

Abstract: A power-bounded operator T satisfying sup n n ‖ T n − T n + 1 ‖ < ∞ $\sup _n n\lVert T^n-T^{n+1}\rVert <\infty $ sup Underscript n Endscripts n StartMetric upper T Superscript n Baseline minus upper T Superscript n plus 1 Baseline EndMetric less than infinity is a Ritt operator. For such operators, we study the generalized square function Q α , s , r T f = ( ∑ n n α | T n ( I − T ) r f | s ) 1 / s $Q_{\alpha ,s,r}^Tf=(\sum _n n^{\alpha } |T^n(I-T)^rf|^s)^{1/s}$ upper Q Subscript alpha comma s comma r Superscript upper T Baseline f equals left parenthesis sigma summation Underscript n Endscripts n Superscript alpha Baseline StartAbsoluteValue upper T Superscript n Baseline left parenthesis upper I minus upper T right parenthesis Superscript r Baseline f EndAbsoluteValue Superscript s Baseline right parenthesis Superscript 1 divided by s . It is known that when T is a positive contraction and a Ritt operator on L p $L^p$ upper L Superscript p , 1 < p < ∞ $1 1 less than p less than infinity , then for any integer r ≥ 1 $r\ge 1$ r greater than or equals 1 , the square function

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2026.10293

Authors: JENNIFER HULTS, KARIN REINHOLD LARSSON

Institution: University at Albany, State University of New York

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

OpenAlex ID: W4416284118