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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 boundednessdoi:10.1155/2013/476309 fatcat:7wyuqi7iyvbkrhcx7d3xwowduy