The generalized Hardy operator with kernel and variable integral limits in Banach function spaces.

Gogatishvili, A.; Lang, J.

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Jensen type inequalities involving homogeneous polynomials.

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Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables

Yongfeng Wu, Andrew Rosalsky, Andrei Volodin (2013)

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The structure of linearly negative quadrant dependent random variables is extended by introducing the structure of $m$ -linearly negative quadrant dependent random variables ( $m = 1, 2, \dots$ ). For a sequence of $m$ -linearly negative quadrant dependent random variables ${X_{n}, n \geq 1}$ and $1 < p < 2$ (resp. $1 \leq p < 2$ ), conditions are provided under which $n^{- 1 / p} \sum_{k = 1}^{n} (X_{k} - E X_{k}) \to 0$ in $L^{1}$ (resp. in $L^{p}$ ). Moreover, for $1 \leq p < 2$ , conditions are provided under which $n^{- 1 / p} \sum_{k = 1}^{n} (X_{k} - E X_{k})$ converges completely to $0$ . The current work extends some results of Pyke and Root (1968) and it extends and...

Displaying similar documents to “The generalized Hardy operator with kernel and variable integral limits in Banach function spaces.”

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Some mean convergence and complete convergence theorems for sequences of m -linearly negative quadrant dependent random variables

Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables