广义Campanato空间上粗糙核参数型Marcinkiewicz积分

作为一类Littlewood-Paley函数,μ_(Ω,b)~ρ(f)是带非齐次粗糙核的参数型Marcinkiewicz积分,其中粗糙核Ω∈L~q(S~(n-1))满足消失性和积分Dini连续,径向核b∈Δ_s(R~+)∩Θ_s(R~n),1q,s∞,复参数ρ具有正实部.仅在一点有限的假设下,该文建立了μ_(Ω,b)~ρ(f)在广义Campanato空间L~(p,φ)(R~n)上的存在性和有界性,本质地推进了众多的已有工作.

Rough Parametric Marcinkiewicz Integrals on Generalized Campanato Spaces

As a Littlewood-Paley function, let μ^ρ_{Ω, b}(f) be the parametric Marcinkiewicz integral with the rough kernel Ω∈L^q(S^n-1) satisfing the cancellation condition and integral Dini continuity, and the radial kernal b ∈?_s(R⁺)∩Θ_s(Rⁿ),  10. Under the only assumption of one point finiteness, the existence and boundedness of μ^ρ_{Ω, b}(f) on the generalized Campanato space L^p, φ(Rⁿ) are obtained. The theorems in this paper substantially extend early results.