Variation and oscillation for semigroups associated with discrete Jacobi operators

TL;DR

This paper establishes weighted $ ext{ell}^p$-inequalities and boundedness properties for variation, oscillation, and maximal operators linked to semigroups of discrete Jacobi operators, enhancing understanding of their convergence behavior.

Contribution

It introduces new weighted $ ext{ell}^p$-inequalities and boundedness results for operators associated with discrete Jacobi semigroups, advancing the analysis of their convergence.

Findings

Weighted $ ext{ell}^p$-inequalities for variation and oscillation operators

Boundedness of maximal operators involving differences of semigroups

Results imply convergence properties of the discrete Jacobi semigroups

Abstract

In this paper we prove weighted $\ell^p$-inequalities for variation and oscillation operators defined by semigroups of operators associated with discrete Jacobi operators. Also, we establish that certain maximal operators involving sums of differences of discrete Jacobi semigroups are bounded on weighted $\ell^p$-spaces. $\ell^p$-boundedness properties for the considered operators provide information about the convergence of the semigroup of operators defining them.