1. Boundedness of variation operators associated with the heat semigroup generated by high order Schr��dinger type operators
- Author
-
Suying Liu and Chao Zhang
- Subjects
Pure mathematics ,General Mathematics ,Mathematics::Analysis of PDEs ,Mathematics::Classical Analysis and ODEs ,General Physics and Astronomy ,Type (model theory) ,01 natural sciences ,symbols.namesake ,Operator (computer programming) ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,0101 mathematics ,High order ,Reverse holder inequality ,Mathematics ,Semigroup ,010102 general mathematics ,42B35, 42B20, 42B25 ,Functional Analysis (math.FA) ,010101 applied mathematics ,Mathematics - Functional Analysis ,Variation (linguistics) ,Mathematics - Classical Analysis and ODEs ,Biharmonic equation ,symbols ,Schrödinger's cat - Abstract
In this paper, we derive the $L^p$-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schr\"odinger type operator $(-\Delta)^2+V^2$. Further more, we prove the boundedness of the variation operators on Morrey spaces. In the proof of the main results, we always make use of the variation inequalities associated with the heat semigroup generated by the biharmonic operator $(-\Delta)^2.$, Comment: 14 pages
- Published
- 2019
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