An improved multiple Cotlar inequality is obtained. From this result, weighted norm inequalities for the maximal operator of a multilinear singular integral including weak and strong estimates are deduced under the multiple weights constructed recently.
Complete -moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete -moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete -moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric...
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