A Generalization of Exponential Class and Its Applications

Hongya Gao, Chao Liu, Hong Tian
2013 Abstract and Applied Analysis  
A function space,Lθ,∞)(Ω),0≤θ<∞, is defined. It is proved thatLθ,∞)(Ω)is a Banach space which is a generalization of exponential class. An alternative definition ofLθ,∞)(Ω)space is given. As an application, we obtain weak monotonicity property for very weak solutions of𝒜-harmonic equation with variable coefficients under some suitable conditions related toLθ,∞)(Ω), which provides a generalization of a known result due to Moscariello. A weighted spaceLwθ,∞)(Ω)is also defined, and the boundedness
more » ... and the boundedness for the Hardy-Littlewood maximal operatorMwand a Calderón-Zygmund operatorTwith respect toLwθ,∞)(Ω)is obtained.
doi:10.1155/2013/476309 fatcat:7wyuqi7iyvbkrhcx7d3xwowduy