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.

中文翻译：

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与离散雅可比算子相关的半群的变分和振荡

在本文中，我们证明了由与离散雅可比算子相关的算子半群定义的变分算子和振荡算子的加权\(\ell ^p\)不等式。此外，我们还确定涉及离散雅可比半群差和的某些最大算子在加权\(\ell ^p\)空间上有界。\(\ell ^p\)所考虑算子的有界性属性提供了有关定义它们的算子半群收敛性的信息。