Localization and compactness of Operators on Fock Spaces

For $0<p\leq\infty$, let $F^{p}_\varphi$ be the Fock space induced by a weight function $\varphi$ satisfying $dd^c \varphi \simeq \omega_0$. In this paper, given $p\in (0, 1]$ we introduce the concept of weakly localized operators on $F^{p}_\varphi$, we characterize the compact operators in the algebra generated by weakly localized operators. As an application, for $0<p<\infty$ we prove that an operator $T$ in the algebra generated by bounded Toeplitz operators with $\textrm{BMO}$ symbols is compact on $F^p_\varphi$ if and only if its Berezin transform satisfies certain vanishing property at $\infty$. In the classical Fock space, we extend the Axler-Zheng condition on linear operators $T$, which ensures $T$ is compact on $F^p_{\alpha}$ for all possible $0<p<\infty$.Comment: 23 Page

Bergman projections on weighted Fock spaces in several complex variables

Abstract Let ϕ be a real-valued plurisubharmonic function on C n ${\mathbb {C}}^{n}$ whose complex Hessian has uniformly comparable eigenvalues, and let F p ( ϕ ) $\mathcal{F}^{p}(\phi)$ be the Fock space induced by ϕ. In this paper, we conclude that the Bergman projection is bounded from the pth Lebesgue space L p ( ϕ ) $L^{p}(\phi )$ to F p ( ϕ ) $\mathcal{F}^{p}(\phi)$ for 1 ≤ p ≤ ∞ $1\leq p \leq\infty$ . As a remark, we claim that Bergman projections are also well defined and bounded on Fock spaces F p ( ϕ ) $\mathcal{F}^{p}(\phi)$ with 0 < p < 1 $0< p<1$ . We also obtain the estimates for the distance induced by ϕ and the L p ( ϕ ) $L^{p}(\phi)$ -norm of Bergman kernel for F 2 ( ϕ ) $\mathcal{F}^{2}(\phi)$

Schatten-Herz class Toeplitz operators on harmonic Bergman spaces of smooth domains in R-n

National Natural Science Foundation of China [10771064, 11101139, 11271124]; Natural Science Foundation of Zhejiang province [Y7080197, Y6090036, Y6100219]; Foundation of Creative Group in Colleges and Universities of Zhejiang Province [T200924]On the setting of the bounded domain Omega in R-n with C infinity boundary, we introduce the Schatten-Herz classes Toeplitz operators. And in term of averaging functions and Berezin transforms, we characterize those finite positive Borel measures on for which the induced Toeplitz operators are in Shatten-Herz classes. As some preliminary results, we obtain the sharp estimate of integral means for the harmonic Bergman kernel on the level surface and the boundedness of the Berezin transform on the Herz spaces

Carleson type measures for harmonic mixed norm spaces with application to Toeplitz operators

National Natural Science Foundation of China [11101139, 11271124]; Natural Science Foundation of Zhejiang Province [Y6090036, Y6100219]; Foundation of Creative Group in Universities of Zhejiang Province [T200924]Let Omega be a bounded domain in a"e (n) with a smooth boundary, and let h (p,q) be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h (p,q) , with which the definition of Carleson type measures for h (p,q) is obtained. And also, the authors obtain the boundedness of the Bergman projection on h (p,q) which turns out the dual space of h (p,q) . As an application, the authors characterize the boundedness (and compactness) of Toeplitz operators T (A mu) on h (p,q) for those positive finite Borel measures A mu

Dynamic Deformation Behavior and Fracture Characteristics of a near &alpha; TA31 Titanium Alloy at High Strain Rates

The quasi-static and dynamic impact compression tests of the TA31 titanium alloy were conducted at the strain rates from 0.001 s&minus;1 to 4000 s&minus;1 and deformation temperatures from 293 K to 773 K, and the TA31 titanium alloy showed typical elastic-plastic characteristics. In the initial stage of compression (elastic deformation), the stress and strain are proportional, and the stress&ndash;strain curve is a straight line. In the plastic deformation stage, the flow stress decreases significantly with the increase of deformation temperature, while the strain rate has no significant effect on the flow stress during dynamic compression. A constitutive model has been established to predict the flow stress, and the relative error is 2.32%. It is shown by observing the microstructure that when the deformation temperature is 293 &deg;C, and the strain rate reaches 1600 s&minus;1, a shear band with an angle of about 45&deg; to the axial direction of the specimen appears, and the severe shear deformation makes the &alpha; phase in the shear band fibrous and contains high-density dislocations. The formation process of the shear band and its influence on fracture are analyzed and discussed

Novel 4-Arm Poly(Ethylene Glycol)-Block-Poly(Anhydride-Esters) Amphiphilic Copolymer Micelles Loading Curcumin: Preparation, Characterization, and In Vitro Evaluation

A novel 4-arm poly(ethylene glycol)-block-poly(anhydride-esters) amphiphilic copolymer (4-arm PEG-b-PAE) was synthesized by esterization of 4-arm poly(ethylene glycol) and poly(anhydride-esters) which was obtained by melt polycondensation of α-, ω-acetic anhydride terminated poly(L-lactic acid). The obtained 4-arm PEG-b-PAE was characterized by 1H-NMR and gel permeation chromatography. The critical micelle concentration of 4-arm PEG-b-PAE was 2.38 μg/mL. The curcumin-loaded 4-arm PEG-b-PAE micelles were prepared by a solid dispersion method and the drug loading content and encapsulation efficiency of the micelles were 7.0% and 85.2%, respectively. The curcumin-loaded micelles were spherical with a hydrodynamic diameter of 151.9 nm. Curcumin was encapsulated within 4-arm PEG-b-PAE micelles amorphously and released from the micelles, faster in pH 5.0 than pH 7.4, presenting one biphasic drug release pattern with rapid release at the initial stage and slow release later. The hemolysis rate of the curcumin-loaded 4-arm PEG-b-PAE micelles was 3.18%, which was below 5%. The IC50 value of the curcumin-loaded micelles against Hela cells was 10.21 μg/mL, lower than the one of free curcumin (25.90 μg/mL). The cellular uptake of the curcumin-loaded micelles in Hela cell increased in a time-dependent manner. The curcumin-loaded micelles could induce G2/M phase cell cycle arrest and apoptosis of Hela cells

Type 2C Phosphatase 1 of Artemisia annua L. Is a Negative Regulator of ABA Signaling

The phytohormone abscisic acid (ABA) plays an important role in plant development and environmental stress response. Additionally, ABA also regulates secondary metabolism such as artemisinin in the medicinal plant Artemisia annua L. Although an earlier study showed that ABA receptor, AaPYL9, plays a positive role in ABA-induced artemisinin content improvement, many components in the ABA signaling pathway remain to be elucidated in Artemisia annua L. To get insight of the function of AaPYL9, we isolated and characterized an AaPYL9-interacting partner, AaPP2C1. The coding sequence of AaPP2C1 encodes a deduced protein of 464 amino acids, with all the features of plant type clade A PP2C. Transcriptional analysis showed that the expression level of AaPP2C1 is increased after ABA, salt, and drought treatments. Yeast two-hybrid and bimolecular fluorescence complementation assays (BiFC) showed that AaPYL9 interacted with AaPP2C1. The P89S, H116A substitution in AaPYL9 as well as G199D substitution or deletion of the third phosphorylation site-like motif in AaPP2C1 abolished this interaction. Furthermore, constitutive expression of AaPP2C1 conferred ABA insensitivity compared with the wild type. In summary, our data reveals that AaPP2C1 is an AaPYL9-interacting partner and involved in the negative modulation of the ABA signaling pathway in A. annua L