关键词: 参数型Marcinkiewicz积分, 广义Campanato空间, 非齐次粗糙核, 存在和有界性

Abstract:

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),  1<q, s<∞, and the parameter ρ ∈C with Re(ρ)>0. 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.

Key words: Parametric Marcinkiewicz integral, Generalized Campanato space, Nonhomogeneous rough kernel, Existence and boundedness