$L^2$ continuity of the Calderón type commutator for the Littlewood-Paley operator with rough variable kernel

Chen, Yanping; Niu, Zhendong; Wang, Liwei

doi:10.2996/kmj/1509415223

Cited by 1 publication

(1 citation statement)

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“…Based on the definition, some fundamental arithmetics, numerical characteristics, including the expectation value and variance, and other properties of rough variables are investigated and proven in succession. By virtue of the theory of rough variables developed by Liu [ 6 ], a great deal of problems in practical applications can be solved admirably (see, e.g., [ 7 , 8 ]).…”

Section: Introductionmentioning

confidence: 99%

Some Inequalities Combining Rough and Random Information

Zhang

2018

Entropy

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Rough random theory, generally applied to statistics, decision-making, and so on, is an extension of rough set theory and probability theory, in which a rough random variable is described as a random variable taking "rough variable" values. In order to extend and enrich the research area of rough random theory, in this paper, the well-known probabilistic inequalities (Markov inequality, Chebyshev inequality, Holder's inequality, Minkowski inequality and Jensen's inequality) are proven for rough random variables, which gives a firm theoretical support to the further development of rough random theory. Besides, considering that the critical values always act as a vital tool in engineering, science and other application fields, some significant properties of the critical values of rough random variables involving the continuity and the monotonicity are investigated deeply to provide a novel analytical approach for dealing with the rough random optimization problems.

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Section: Introductionmentioning

confidence: 99%