In this paper, the general Marcinkiewicz integral operator μ Ω,α on the H p Sobolev spaces under the proper condition of kernel Ω(x′) is considered. It is obtained that μ Ω,α is bounded from H p ...In this paper, the general Marcinkiewicz integral operator μ Ω,α on the H p Sobolev spaces under the proper condition of kernel Ω(x′) is considered. It is obtained that μ Ω,α is bounded from H p α to L p for some 0<p≤1.展开更多
Let Ω be a bounded convex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△on Ω Let hPT(Ω) = {f∈D'(Ω) : (?)F ∈ hP(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hard...Let Ω be a bounded convex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△on Ω Let hPT(Ω) = {f∈D'(Ω) : (?)F ∈ hP(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f Ω(?)2(Gf) for every f ∈hPr(Ω) is obtained, where n/(n + 1) <p≤1.展开更多
基金Jiang and Jia were supported in part by Education Departmentof Zhejiang province
文摘In this paper, the general Marcinkiewicz integral operator μ Ω,α on the H p Sobolev spaces under the proper condition of kernel Ω(x′) is considered. It is obtained that μ Ω,α is bounded from H p α to L p for some 0<p≤1.
文摘Let Ω be a bounded convex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△on Ω Let hPT(Ω) = {f∈D'(Ω) : (?)F ∈ hP(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f Ω(?)2(Gf) for every f ∈hPr(Ω) is obtained, where n/(n + 1) <p≤1.
