arXiv subjects
Publications and source records attributed to Hua Wang.
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 $1/q=1/p-α/n$.
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 article, we will introduce weighted Hardy spaces $H^p_L(w)$ associated with $L$ by means of the area integral function and study their atomic decomposition theory. We also show that the Riesz transform $\nabla L^{-1/2}$ associated with $L$ is bounded from our new space $H^p_L(w)$ to the classical weighted Hardy space $H^p(w)$ when $\frac{n}{n+1}<p<1$ and$w\in A_1\cap RH_{(2/p)'}$.
Let $Ω\in L^q(S^{n-1})$ with $1<q\le\infty$ be homogeneous of degree zero and has mean value zero on $S^{n-1}$. In this paper, we will study the boundedness of homogeneous singular integrals and Marcinkiewicz integrals with rough kernel on the weighted Morrey spaces $L^{p,κ}(w)$ for $q'\le p<\infty$(or $q'<p<\infty$) and $0<κ<1$. We will also prove that the commutator operators formed by a $BMO(\mathbb R^n)$ function $b(x)$ and these rough operators are bounded on the weighted Morrey spaces $L^{p,κ}(w)$ for $q'<p<\infty$ and $0<κ<1$.
In this paper, by using the atomic decomposition theory of weighted Hardy spaces, we will give some weighted weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley $g$-function and $g^*_λ$-function on these spaces.
In this paper, we will study the boundedness of intrinsic square functions on the weighted Hardy spaces $H^p(w)$ for $0<p<1$, where $w$ is a Muckenhoupt's weight function. We will also give some intrinsic square function characterizations of weighted Hardy spaces $H^p(w)$ for $0<p<1$.
In this paper, the cosmological dynamics of a modified holographic dark energy which is derived from the UV/IR duality by considering the black hole mass in higher dimensions as UV cutoff, is investigated in Dvali-Gabadaze-Porrati (DGP) brane world model. We choose Hubble horizon and future event horizon as IR cutoff respectively. And the two branches of the DGP model are both taken into account. When Hubble horizon is considered as IR cutoff, the modified holographic dark energy (HDE) behaves like an effect dark energy that modification of gravity in pure DGP brane world model acts and it can drive the expansion of the universe speed up at late time in $ε=-1$ branch which in pure DGP model can not undergo an accelerating phase. When future event horizon acts as IR cutoff, the equation of state parameter of the modified HDE can cross the phantom divide.
The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate achemical compound's molecular graph with experimentally gathered data regarding the compound's characteristics. The tree that minimizes the Wiener index among trees of given maximal degree was studied. We characterize trees that achieve the maximum and minimum Wiener index, given the number of vertices and the degree sequence.
The capacity of the two-user Gaussian interference channel has been open for thirty years. The understanding on this problem has been limited. The best known achievable region is due to Han-Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a simplified Han-Kobayashi type scheme can achieve to within a single bit the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high SNR regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.
We study the single top quark production process in various kinds of technicolor models in high energy positron photon collisions at the future electron positron linear colliders. It is shown that if there is certain charged pseudo Goldstone boson (PGB) coupling to t(anti-b), the t(anti-b)-channel PGB contribution is dominant, but the situation is quite different from that in the neutral channel, t(anti-t) production in photon photon collisions, due to the destructive nature of different amplitudes. At the DESY limear collider TESLA, the event rates in models with t(anti-b)-channel PGB contributions, such as the top-color-assisted technicolor model, etc. are experimentally measurable. This process provides a feasible test of technicolor models with t(abti-b)-channel PGB contributions.
Pseudo-Goldstone boson contributions to $t\bar{t}$ production rates in technicolor models with and without topcolor at the $\sqrt{s}=0.5 and 1.5$ TeV photon colliders and hadron colliders are reviewed. For reasonable ranges of the parameters, the contributions are large enough to be experimentally observable. Models with topcolor, without topcolor and the MSSM with $\tanβ\geq 1$ can be experimentally distinguished.
We study pseudo-Goldstone boson corrections to top quark pair production rates in technicolor models with and without topcolor at the E=0.5 teV and 1.5 TeV photon colliders. We find that, for reasonable ranges of the parameters, the corrections are large enough to be observable, and the corrections in models with topcolor are considerably larger than those in models without topcolor, and they are all significantly larger than the corresponding corrections in the minimal supersymmetric standard model (MSSM) with tan(beta) of the order of 1. So that the two kinds of technicolor models and the MSSM with tan(beta) of the order of 1 can be experimentally distinguished.
Supersymmetric QCD corrections to top quark pair production by photon fusion are calculated in the minimal supersymmetric standard model taking into account of the effects of stops in the corrections to the total cross-section of t anti-t production at the future electron-positron linear collider. We find that the relative correction can be a few percent for reasonable values of the parameters.