Huoxiong Wu
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View article: Strichartz estimates involving orthonormal systems at the critical summability exponent
Strichartz estimates involving orthonormal systems at the critical summability exponent Open
The primary objective of this paper is to investigate the orthonormal Strichartz estimates at the critical summability exponent for the Schrödinger operator $e^{itΔ}$ with initial data from the homogeneous Sobolev space $\dot{H}^s (\mathbb…
View article: Orthonormal Strichartz estimates for Dunkl-Schrödinger equation of initial data with Sobolev regularity
Orthonormal Strichartz estimates for Dunkl-Schrödinger equation of initial data with Sobolev regularity Open
Let $Δ_κ$ be the Dunkl-Laplacian on $\mathbb{R}^n$. The main aim of this paper is to investigate the orthonormal Strichartz estimates for the Schrödinger equation with initial data from the homogeneous Dunkl-Sobolev space $\dot{H}_κ^s (\ma…
View article: Matrix weighted inequalities for fractional type integrals associated to operators with new classes of weights
Matrix weighted inequalities for fractional type integrals associated to operators with new classes of weights Open
Let $e^{-tL}$ be a analytic semigroup generated by $-L$, where $L$ is a non-negative self-adjoint operator on $L^2(\mathbb{R}^d)$. Assume that the kernels of $e^{-tL}$, denoted by $p_t(x,y)$, only satisfy the upper bound: for all $N>0$, th…
View article: The uniform quantitive weighted boundedness of fractional Marcinkiewicz integral and its commutator
The uniform quantitive weighted boundedness of fractional Marcinkiewicz integral and its commutator Open
Suppose that $Ω\in L^{\infty}(\mathbb{S} ^{n-1})$ is homogeneous of degree zero with mean value zero. Then we consider a fractional type Marcinkiewicz integral operator $$μ_{Ω,β}f(x) = \left ( \int_{0}^{\infty } \left | \int_{\left | x-y \…
View article: Weighted variational inequalities for heat semigroups associated with Schrödinger operators related to critical radius functions
Weighted variational inequalities for heat semigroups associated with Schrödinger operators related to critical radius functions Open
Let $\mathcal{L}$ be a Schrödinger operator and $\mathcal{V}_\varrho(e^{-t\mathcal{L}})$ be the variation operator of heat semigroup associated to $\mathcal{L}$ with $\varrho>2$. In this paper, we first obtain the quantitative weighted $L^…
View article: Orthonormal Strichartz inequalities and their applications on abstract measure spaces
Orthonormal Strichartz inequalities and their applications on abstract measure spaces Open
The main objective of this paper is to extend certain fundamental inequalities from a single function to a family of orthonormal systems. In the first part of the paper, we consider a non-negative, self-adjoint operator $L$ on $L^2(X,μ)$, …
View article: The commutators of multilinear fractional Calderón-Zygmund operators on weighted Hardy spaces
The commutators of multilinear fractional Calderón-Zygmund operators on weighted Hardy spaces Open
In this paper, we study the behaviors of the commutators [\vec~b,T_\gamma] generated by multilinear fractional Calderón-Zygmund operators T_γ with vec b=(b_1,…,b_m)∈ (L_loc¹)^m on weighted Hardy spaces. Generally, for vec b∈ (BMO)^m, [\vec…
View article: Decay estimates for a class of semigroups related to self-adjoint operators on metric measure spaces
Decay estimates for a class of semigroups related to self-adjoint operators on metric measure spaces Open
Assume that $(X,d,μ)$ is a metric space endowed with a non-negative Borel measure $μ$ satisfying the doubling condition and the additional condition that $μ(B(x,r))\gtrsim r^n$ for any $x\in X, \,r>0$ and some $n\geq1$. Let $L$ be a non-ne…
View article: Global Well-posedness of the free boundary problem for the compressible Euler equations with damping and gravity
Global Well-posedness of the free boundary problem for the compressible Euler equations with damping and gravity Open
We consider the free boundary problem for a compressible barotropic fluid lying above a rigid bottom and below the air, in a horizontally periodic setting. The fluid dynamics is governed by the compressible Euler equations with damping and…
View article: On the Commutators of Marcinkiewicz Integral with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces
On the Commutators of Marcinkiewicz Integral with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces Open
This paper is devoted to exploring the mapping properties for the commutator μΩ,b generated by Marcinkiewicz integral μΩ with a locally integrable function b in the generalized Campanato spaces on the generalized Morrey spaces. Under the a…
View article: Well-posedness of Navier-Stokes equations established by the decaying speed of single norm
Well-posedness of Navier-Stokes equations established by the decaying speed of single norm Open
The decaying speed of a single norm more truly reflects the intrinsic harmonic analysis structure of the solution of the classical incompressible Navier-Stokes equations. No previous work has been able to establish the well-posedness under…
View article: On the Bounds of Weak $(1,1)$ Norm of Hardy-Littlewood Maximal Operator with $L\log L({\mathbb S^{n-1}})$ Kernels
On the Bounds of Weak $(1,1)$ Norm of Hardy-Littlewood Maximal Operator with $L\log L({\mathbb S^{n-1}})$ Kernels Open
Let $Ω\in L^1{({\mathbb S^{n-1}})}$, be a function of homogeneous of degree zero, and $M_Ω$ be the Hardy-Littlewood maximal operator associated with $Ω$ defined by $M_Ω(f)(x) = \sup_{r>0}\frac1{r^n}\int_{|x-y|λ\}| = n^{-1}\|Ω\|_{L^1({\math…
View article: A remark on ill-posedness
A remark on ill-posedness Open
Norm inflation implies certain discontinuous dependence of the solution on the initial value. The well-posedness of the mild solution means the existence and uniqueness of the fixed points of the corresponding integral equation. For ${\rm …
View article: Bump conditions and two-weight inequalities for commutators of fractional integrals
Bump conditions and two-weight inequalities for commutators of fractional integrals Open
This paper gives new two-weight bump conditions for the sparse operators related to iterated commutators of fractional integrals. As applications, the two-weight bounds for iterated commutators of fractional integrals under more general bu…
View article: Limiting weak-type behaviors for singular integrals with rough $L\log L(\mathbb{S}^n)$ kernels
Limiting weak-type behaviors for singular integrals with rough $L\log L(\mathbb{S}^n)$ kernels Open
Let $Ω$ be a function of homogeneous of degree zero and vanish on the unit sphere $\mathbb {S}^n$. In this paper, we investigate the limiting weak-type behavior for singular integral operator $T_Ω$ associated with rough kernel $Ω$. We show…
View article: A note on extrapolation of compactness
A note on extrapolation of compactness Open
This note is devoted to the study of Hytönen's extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight setting are obtained. As applications, we obtain two-weight …
View article: Sparse dominations and weighted variation inequalities for singular integrals and commutators
Sparse dominations and weighted variation inequalities for singular integrals and commutators Open
This paper gives the pointwise sparse dominations for variation operators of singular integrals and commutators with kernels satisfying the $L^r$-Hörmander conditions. As applications, we obtain the strong type quantitative weighted bounds…
View article: The limiting weak type behaviors and The lower bound for a new weak $L\log L$ type norm of strong maximal operators
The limiting weak type behaviors and The lower bound for a new weak $L\log L$ type norm of strong maximal operators Open
It is well known that the weak ($1,1$) bounds doesn't hold for the strong maximal operators, but it still enjoys certain weak $L\log L$ type norm inequality. Let $Φ_n(t)=t(1+(\log^+t)^{n-1})$ and the space $L_{Φ_n}({\mathbb R^{n}})$ be the…
View article: Limiting weak-type behavior for rough bilinear operators
Limiting weak-type behavior for rough bilinear operators Open
Let $Ω_1,Ω_2$ be functions of homogeneous of degree $0$ and $\vecΩ=(Ω_1,Ω_2)\in L\log L(\mathbb{S}^{n-1})\times L\log L(\mathbb{S}^{n-1})$. In this paper, we investigate the limiting weak-type behavior for bilinear maximal function $M_{\ve…
View article: Variational characterizations of weighted Hardy spaces and weighted $BMO$ spaces
Variational characterizations of weighted Hardy spaces and weighted $BMO$ spaces Open
This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.
View article: A revisit on the compactness of commutators
A revisit on the compactness of commutators Open
A new characterization of $\text {CMO}(\mathbb R^n)$ is established replying upon local mean oscillations. Some characterizations of iterated compact commutators on weighted Lebesgue spaces are given, which are new even in the unweighted s…
View article: Mixed radial-angular integrability for rough singular integrals and maximal operators
Mixed radial-angular integrability for rough singular integrals and maximal operators Open
This paper is devoted to studying singular integrals and maximal operators with rough kernels in the mixed homogeneity setting. Assuming the kernels satisfy certain rather weak sized conditions, the boundedness for such operators on the mi…
View article: Weighted estimates for rough singular integrals with applications to angular integrability, II
Weighted estimates for rough singular integrals with applications to angular integrability, II Open
This paper is devoted to studying certain singular integral operators with rough radial kernel h and sphere kernel Ω as well as the corresponding maximal operators along polynomial curves.The authors establish several weighted estimates fo…
View article: On commutators of certain fractional type integrals with Lipschitz functions
On commutators of certain fractional type integrals with Lipschitz functions Open
In this paper, we study the commutators generated by Lipschitz functions and fractional type integral operators with kernels of the form Kα(x,y)=κ1(x−A1y)κ2(x−A2y)⋯κm(x−Amy), $$ K_{\alpha }(x,y) = \kappa _{1}(x - A_{1}y) \kappa _{2}(x - A_…
View article: On the compactness of oscillation and variation of commutators
On the compactness of oscillation and variation of commutators Open
In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new $CMO(\mathbb{R}^n)$ characterization via …
View article: On Positive solutions of integral equations with the weighted Bessel potentials
On Positive solutions of integral equations with the weighted Bessel potentials Open
This paper is devoted to exploring the properties of positive solutions for a class of nonlinear integral equation(s) involving the Bessel potentials, which are equivalent to certain partial differential equations under appropriate integra…
View article: On the Limiting Weak-type Behaviors for Maximal Operators Associated with Power Weighted Measure
On the Limiting Weak-type Behaviors for Maximal Operators Associated with Power Weighted Measure Open
Let $\unicode[STIX]{x1D6FD}\geqslant 0$ , let $e_{1}=(1,0,\ldots ,0)$ be a unit vector on $\mathbb{R}^{n}$ , and let $d\unicode[STIX]{x1D707}(x)=|x|^{\unicode[STIX]{x1D6FD}}dx$ be a power weighted measure on $\mathbb{R}^{n}$ . For $0\leqsl…
View article: Characterizations of the compactness of commutators associated with Lipschitz functions
Characterizations of the compactness of commutators associated with Lipschitz functions Open
We first give some characterizations of the the compact iterated commutators associated with Lipschitzs functions. Our results are even new in the unweighted setting for the first order commutators.