Variation and oscillation for semigroups associated with discrete Jacobi operators

In this paper we prove weighted ${\mathrm{\ell }}^p$-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 ${\mathrm{\ell }}^p$-spaces. ${\mathrm{\ell }}^p$-boundedness properties for the considered operators provide information about the convergence of the semigroup of operators defining them.