arXiv subjects
Publications and source records attributed to Hua Wang.
Let $T_Ω$ be the singular integral operator with variable kernel $Ω(x,z)$. In this paper, by using the atomic decomposition theory of weighted weak Hardy spaces, we will obtain the boundedness properties of $T_Ω$ on these spaces, under some Dini type conditions imposed on the variable kernel $Ω(x,z)$.
In this paper, we will obtain the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_λ$-function on the weighted Herz spaces $\dot K^{α,p}_q(w_1,w_2)$ ($K^{α,p}_q(w_1,w_2)$) with general weights.
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in applications. The number of subtrees in the extremal cases constitute sequences which are of interest to number theorists. The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously. Most recently, results of this nature are generalized to trees with a given degree sequence. In this note, we characterize the trees which maximize the number of subtrees among trees of a given order and degree sequence. Instead of using theoretical arguments, we take an algorithmic approach that explicitly describes the process of achieving an extremal tree from any random tree. The result also leads to some interesting questions and provides insight on finding the trees close to extremal and their numbers of subtrees.
This paper investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalizes the recent results of Kirk and Wang. These trees coincide with those which were proven by Wang and independently Zhang et al. to minimize the Wiener index. We also provide a partial ordering of the extremal trees with different degree sequences, some extremal results follow as corollaries.
In this paper, we will study the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_λ$-function on the weighted Morrey spaces $L^{p,κ}(w)$ for $1<p<\infty$ and $0<κ<1$. The corresponding commutators generated by $BMO(\mathbb R^n)$ functions and intrinsic square functions are also discussed.
Let $w$ be a Muckenhoupt weight and $H^p_w(\mathbb R^n)$ be the weighted Hardy spaces. In this paper, by using the atomic decomposition of $H^p_w(\mathbb R^n)$, we will show that the Bochner-Riesz operators $T^δ_R$ are bounded from $H^p_w(\mathbb R^n)$ to the weighted weak Hardy spaces $WH^p_w(\mathbb R^n)$ when $0<p<1$ and $δ=n/p-(n+1)/2$. This result is new even in the unweighted case.
In this paper, we will obtain the weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_λ$-function on the weighted Morrey spaces $L^{1,κ}(w)$ for $0<κ<1$ and $w\in A_1$.
In this paper, we will study the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_λ$-function on the generalized Morrey spaces $L^{p,Φ}$ for $1\le p<\infty$, where $Φ$ is a growth function on $(0,\infty)$ satisfying the doubling condition. The boundedness of the commutators generated by $BMO(\mathbb R^n)$ functions and intrinsic square functions is also obtained.
In this paper, by using the atomic decomposition theorem for weighted weak Hardy spaces, we will show the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_λ$-function on these spaces.
We provide a recursive classification of meander graphs, showing that each meander is identified by a unique sequence of fundamental graph-theoretic moves. This sequence is called the meander's signature. The signature not only provides a fast algorithm for the computation of the index of a Lie algebra associated with the meander, but also allows for the speedy determination of the graph's plane homotopy type - a finer invariant than the index. The signature can be used to construct arbitrarily large sets of meanders, Frobenius and otherwise, of any given size and configuration. Making use of a more refined signature, we are able to prove an important conjecture of Gerstenhaber & Giaquinto: The spectrum of the adjoint of a principal element in a Frobenius seaweed Lie algebra consists of an unbroken chain of integers. Additionally, we show the dimensions of the associated eigenspaces to be unimodal. In certain special cases, the signature is used to produce an explicit formula for the index of a seaweed Lie subalgebra of sl(n) in terms of elementary functions.
The Marcinkiewicz integral is essentially a Littlewood-Paley $g$-function, which plays a important role in harmonic analysis. In this article, by using the atomic decomposition theory of weighted Hardy spaces and homogeneous weighted Herz-type Hardy spaces, we will obtain some weighted weak type estimates for Marcinkiewicz integrals on these spaces.
Let $w$ be a Muckenhoupt weight and $WH^p_w(\mathbb R^n)$ be the weighted weak Hardy spaces. In this paper, by using the atomic decomposition of $WH^p_w(\mathbb R^n)$, we will show that the maximal Bochner-Riesz operators $T^δ_*$ are bounded from $WH^p_w(\mathbb R^n)$ to $WL^p_w(\mathbb R^n)$ when $0 n/p-{(n+1)}/2$. Moreover, we will also prove that the Bochner-Riesz operators $T^δ_R$ are bounded on $WH^p_w(\mathbb R^n)$ for $0 n/p-{(n+1)}/2$. Our results are new even in the unweighted case.
We extend the set of known infinite families of Frobenius seaweed Lie subalgebras of $\mathfrak{sl}_{n}$ to include a family which is the first non-trivial general family containing algebras whose associated meanders have an arbitrarily large number of parts.
Let $M_{Ω,α}$ and $T_{Ω,α}$ be the fractional maximal and integral operators with rough kernels, where $0<α<n$. In this paper, we shall study the continuity properties of $M_{Ω,α}$ and $T_{Ω,α}$ on the weighted Morrey spaces $L^{p,κ}(w)$. The boundedness of their commutators with BMO functions is also obtained.
Let $T$ be a Calderón-Zygmund singular integral operator. In this paper, we will show some weighted boundedness properties of commutator $[b,T]$ on the weighted Morrey spaces $L^{p,κ}(w)$ under appropriate conditions on the weight $w$, where the symbol $b$ belongs to weighted $BMO$ or Lipschitz space or weighted Lipschitz space.
Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbb R^n)$ with Gaussian kernel bound, and let $L^{-α/2}$ be the fractional integrals of $L$ for $0<α<n$. In this paper, we will obtain some boundedness properties of commutators $\big[b,L^{-α/2}\big]$ on the weighted Morrey spaces $L^{p,κ}(w)$ when the symbol $b$ belongs to $BMO(\mathbb R^n)$ or homogeneous Lipschitz space.
In this paper, we study a curvaton model where the curvaton is acted by Galileon field. We calculate the power spectrum of fluctuation of G-curvaton during inflation and discuss how it converts to the curvature perturbation after the end of inflation. We estimate the bispectrum of curvature perturbation induced, and show the dependence of non-Gaussianity on the parameters of model. It is found that our model can have sizable local and equilateral non-Gaussianities to up to ${\cal O}(10^2)$, which is illustrated by an explicit example.
Let $L=-Δ+V$ be a Schrödinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this paper, we first define molecules for weighted Hardy spaces $H^p_L(w)$($0<p\le1$) associated to $L$ and establish their molecular characterizations. Then by using the atomic decomposition and molecular characterization of $H^p_L(w)$, we will show that the imaginary power $L^{iγ}$ is bounded on $H^p_L(w)$ for $n/{(n+1)}<p\le1$, and the fractional integral operator $L^{-α/2}$ is bounded from $H^p_L(w)$ to $H^q_L(w^{q/p})$, where $0<α<\min\{n/2,1\}$, $n/{(n+1)}<p\le n/{(n+α)}$ and $1/q=1/p-α/n$.