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In this paper we prove weighted $\ell^p$-inequalities for variation andoscillation operators defined by semigroups of operators associated withdiscrete Jacobi operators. Also, we establish that certain maximal operatorsinvolving sums of differences of discrete Jacobi semigroups are bounded onweighted $\ell^p$-spaces. $\ell^p$-boundedness properties for the consideredoperators provide information about the convergence of the semigroup ofoperators defining them.

Variation and oscillation for semigroups associated with discrete Jacobi operators