arXiv subjects

Lisheng Shu

Publications and source records attributed to Lisheng Shu.

3 recordsLinked to original sources

arXiv2021

The factorizations of $H^ρ(\mathbb{R}^n)$ via multilinear Calderón-Zygmund operators on weighted Lebesgue spaces

We extend the recently much-studied Hardy factorization theorems to the weight case. The key point of this paper is to establish the factorization theorems without individual condition on the weight functions. As a direct application, we obtain the characterizations of $BMO(\mathbb{R}^n)$ space and Lipschitz spaces via the weighted boundedness of commutators of multilinear Calderón-Zygmund operators with the genuinely multilinear weights.

math.FA↗

arXiv2021

New function classes of Morrey-Campanato type and their applications

The aim of this paper is to introduce and investigative some new function classes of Morrey-Campanato type. Let $0 0}ρ^{-λ}\int_{Ω(x_{0},ρ)}\big|f(x)-|f|_{Ω(x_{0},ρ)}\big|^pdx<\infty,$$ where $Ω(x_{0},ρ)=Q(x_{0},ρ)\cap Ω$ and $Q(x,ρ)$ is denote the cube of $\mathbb{R}^n$. Some basic properties and characterizations of these classes are presented. If $0\leq λ<n$, the space is equivalent to related Morrey space. If $λ=n$, then $f \in \mathcal{\bar{L}}^{p,n}(Ω)$ if and only if $f\in BMO(Ω)$ with $f^{-}\in L^{\infty}(Ω)$, where $f^{-}=-\min\{0,f\}$. If $n<λ\leq n+p$, the $\mathcal{\bar{L}}^{p,λ}(Ω)$ functions establish an integral characterization of the nonnegative Hölder continue functions. As applications, this paper gives unified criterions on the necessity of bounded commutators of maximal functions.

math.FA↗

arXiv2013

Boundedness of fractional integral operators on non-homogeneous metric measure spaces

In this paper, the fractional integral operator on non-homogeneous metric measure spaces is introduced, which contains the classic fractional integral operator, fractional integral with non-doubling measures and fractional integral with fractional kernel of order $α$ and regularity $ε$ introduced by García-Cuerva and Gatto as special cases. And the $(L^{p}(μ),L^{q}(μ))$-boundedness for fractional integral operators on non-homogeneous metric measure spaces is established. From this, the $(L^{p}(μ),L^{q}(μ))$-boundedness for commutators and multilinear commutators generated by fractional integral operators with $RBMO(μ)$ function are further obtained. These results in this paper includes the corresponding results on both the homogeneous spaces and non-doubling measure spaces.

math.FA↗