一类积分算子在加权Campanato空间的有界性(英文)

Boundedness of Littlewood-Paley Operators and Marcinkiewicz Integral on WeightedCamanato Space ε_ω^(α,ρ)

本文证明了下述结果:在适当条件下,若f∈ε_(?)～(?)(?),则g(f)(x)(s(f)(x),μ(f)(x))=∞,a,e.x∈R～(?)或g(f)(x)(s(f)(x),g_(?)～(?)(f)(x),μ(f)(x))<∞,a,e.x∈R～(?),在后一种情形,我们有g(f)(s(f),g_(?)～(?)(f),μ(f))∈ε_(?)～(?)(?)且‖g(f)‖(?)(‖s(f)(?)‖g_λ～(?)(f)‖(?)‖μ(f)‖(?))≤c‖f‖(?)其中C是不赖于f(x)的常数.

The main results obtained in this paper are follows: under suitable conditions, if f(x), then either g(f)(x)(s(f)(x), (f)(x), μ(f)(x)) ≡∞, α.e.xRn or g(f)(x)(s(f)(x), g*(f)(x),μ(f)(x))&lt;∞, α.e.x∈Rn, in the later case, we have g(f)(x)(s(f)(x),g (f)(x), μ(f)(x))∈, furthermore,where C is a constant independent of f(x).