arXiv subjects
Publications and source records attributed to Shuangping Tao.
In this paper, we are devoted to studying some sharp bounds for Hardy type operators on mixed radial-angular type function spaces. In addition, we will establish the sharp weak-type estimates for the fractional Hardy operator and its conjugate operator, respectively.
This paper is devoted to studying the regularity properties for the new maximal operator $M_φ$ and the fractional new maximal operator $M_{φ,β}$ in the local case. Some new pointwise gradient estimates of $M_{φ,Ω}$ and $M_{φ,β,Ω}$ are given. Moreover, the boundedness of $M_{φ,Ω}$ and $M_{φ,β,Ω}$ on Sobolev space is established. As applications, we also obtain the bounds of the above operators on Sobolev space with zero boundary values.
The aim of this paper is to obtain the boundedness of some operator on grand generalized weighted Morrey spaces $\mathcal{L}^{p),ϕ}_φ(ω)$ over RD-spaces. Under assumption that functions $φ$ and $ϕ$ satisfy certain conditions, the authors prove that Hardy-Littlewood maximal operator and $θ$-type Calderón-Zygmund operator are bounded on grand generalized weighted Morrey spaces $\mathcal{L}^{p),ϕ}_φ(ω)$. Moreover, the boundedness of commutator $[b,T_θ]$ which is generated by $θ$-type Calderón-Zygmund operator $T_θ$ and $b\in\mathrm{BMO}(μ)$ on spaces $\mathcal{L}^{p),ϕ}_φ(ω)$ is also established. The results regarding the grand generalized weighted Morrey spaces is new even for domains of Euclidean spaces.
An RD-space $\mathcal{X}$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in $\mathcal{X}$. In this setting, the authors establish the boundedness of bilinear $θ$-type Calderón-Zygmund operator $T_θ$ and its commutator $[b_1,b_2,T_θ]$ generated by the function $b_1,b_2\in BMO(μ)$ and $T_θ$ on generalized weighted Morrey space $\mathcal{M}^{p,ϕ}(ω)$ and generalized weighted weak Morrey space $W\mathcal{M}^{p,ϕ}(ω)$ over RD-spaces.