Searcharxiv⌕ Search

arXiv subjects

Jianglong Wu

Publications and source records attributed to Jianglong Wu.

7 recordsLinked to original sources
arXiv2020

Characterization of Lipschitz Functions via Commutators of Multilinear Singular Integral Operators in Variable Lebesgue Spaces

In this paper, the main aim is to consider the boundedness of commutators of multilinear Calderón-Zygmund operators with Lipschitz functions in the context of the variable exponent Lebesgue spaces. Furthermore, the variable versions of the Lipschitz spaces are also discussed, and with the help of a key tool of a pointwise estimate involving the sharp maximal operator of the multilinear fractional commutator and certain associated maximal operators.

math.CA↗
arXiv2019

Some notes on commutators of the fractional maximal function on variable Lebesgue spaces

Let $0<α<n$ and $M_α$ be the fractional maximal function. The nonlinear commutator of $M_α$ and a locally integrable function $b$ is given by $[b,M_α](f)=bM_α(f)-M_α(bf)$. In this paper, we mainly give some necessary and sufficient conditions for the boundedness of $[b,M_α]$ on variable Lebesgue spaces when $b$ belongs to Lipschitz or $BMO(\rn)$ spaces, by which some new characterizations for certain subclasses of Lipschitz and $BMO(\rn)$ spaces are obtained.

math.CA↗
arXiv2014

Boundedness for fractional Hardy-type operator on Herz-Morrey spaces with variable exponent

In this paper, the fractional Hardy-type operator of variable order $β(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}_{p_{_{1}},q_{_{1}}(\cdot)}^{α,λ}(\mathbb{R}^{n})$ with variable exponent $q_{1}(x)$ into the weighted space $M\dot{K}_{p_{_{2}},q_{_{2}}(\cdot)}^{α,λ}(\mathbb{R}^{n},ω)$, where $ω=(1+|x|)^{-γ(x)}$ with some $γ(x)>0$ and $ 1/q_{_{1}}(x)-1/q_{_{2}}(x)=β(x)/n$ when $q_{_{1}}(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_{_{1}}(x)$ satisfies the logarithmic continuity condition both locally and at infinity that $1< q_{1}(\infty)\le q_{1}(x)\le( q_{1})_{+}<\infty~(x\in \mathbb{R}^{n})$.

math.FA↗
arXiv2013

Weighted Endpoint Estimates for Multilinear Commutators of Marcinkiewicz Integrals

Let $μ_{Ω,\vec{b}}$ be the multilinear commutator generalized by $μ_Ω$, the $n$-dimensional Marcinkiewicz integral, with $\Osc_{\exp L^{^τ}}(\R^{n})$ functions for $τ\ge 1$, where $\Osc_{\exp L^{^τ}}(\R^{n})$ is a space of Orlicz type satisfying that $\Osc_{\exp L^{^τ}}(\R^{n})=\BMO(\R^{n})$ if $τ=1$ and $\Osc_{\exp L^{^τ}}(\R^{n})\subset\BMO(\R^{n})$ if $τ>1$. The authors establish the weighted weak $L\log L$-type estimates for $μ_{Ω,\vec{b}}$ when $Ω$ satisfies a kind of Dini conditions.

math.FA↗
arXiv2013

Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel

Let $μ_{Ω,\vec{b}}$ be the multilinear commutator generalized by $μ_Ω$, the $n$-dimensional Marcinkiewicz integral with the bounded kernel, and $b_{j}\in \Osc_{\exp L^{r_{j}}}(1\le j\le m)$. In this paper, the following weighted inequalities are proved for $ω\in A_{\infty}$ and $0<p<\infty$, $$\|μ_Ω(f)\|_{L^{p}(ω)}\leq C\|M(f)\|_{L^{p}(ω)}, \ \ \|μ_{Ω,\vec{b}}(f)\|_{L^{p}(ω)}\leq C\|M_{L(\log L)^{1/r}}(f)\|_{L^{p}(ω)}.$$ The weighted weak $L(\log L)^{1/r}$ -type estimate is also established when $p=1$ and $ω\in A_{1}$.

math.FA↗