Schatten Class Hankel Operators on Weighted Bergman Spaces induced by regular weights

In this paper, for $1\leq p<\infty$, we provide several descriptions of Schatten $p$-class Hankel operators $H_f$ and $H_{\overline{f}}$ on the weight Bergman space $A^2_\omega$, in terms of a certain global and local mean oscillation of the symbol $f\in L^2_\omega$, provided $\omega$ is a class of regular weights. The approaches applied to rely on several classical methods, and simultaneously rely on a novel but more convenient construction associated with the atomic decomposition of $A^2_\omega$.Comment: 14 pages, any comments/addition would be appreciate

Volterra-type operators mapping weighted Dirichlet space into H∞H^\infty

The problem of describing the analytic functions $g$ on the unit disc such that the integral operator $T_g(f)(z)=\int_0^zf(\zeta)g'(\zeta)\,d\zeta$ is bounded (or compact) from a Banach space (or complete metric space) $X$ of analytic functions to the Hardy space $H^\infty$ is a tough problem and remains unsettled in many cases. For analytic functions $g$ with non-negative Maclaurin coefficients, we describe the boundedness and compactness of $T_g$ acting from a weighted Dirichlet space $D^p_\omega$, induced by an upper doubling weight $\omega$, to $H^\infty$. We also characterize, in terms of neat conditions on $\omega$, the upper doubling weights for which $T_g: D^p_\omega\to H^\infty$ is bounded (or compact) only if $g$ is constant

Integral Operators Induced by Symbols with Non-negative Maclaurin Coefficients Mapping into H∞

For analytic functions g on the unit disk with non-negative Maclaurin coefficients, we describe the boundedness and compactness of the integral operator Tg( f )(z) = z 0 f (ζ )g(ζ ) dζ from a space X of analytic functions in the unit disk to H∞, in terms of neat and useful conditions on the Maclaurin coefficients of g. The choices of X that will be considered contain the Hardy and the Hardy–Littlewood spaces, the Dirichlet-type spaces Dp p−1, as well as the classical Bloch and BMOA spaces.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Funding for open access charge: Universidad de Málaga / CBU

Two weight inequality for Hankel form on weighted Bergman spaces induced by doubling weights

The boundedness of the small Hankel operator $h_f^\nu(g)=P_\nu(f\bar{g})$, induced by an analytic symbol $f$ and the Bergman projection $P_\nu$ associated to $\nu$, acting from the weighted Bergman space A^p_\om to $A^q_\nu$ is characterized on the full range $0<p,q<\infty$ when $\omega,\nu$ belong to the class $\mathcal{D}$ of radial weights admitting certain two-sided doubling conditions. Certain results obtained are equivalent to the boundedness of bilinear Hankel forms, which are in turn used to establish the weak factorization $A_{\eta}^{q}=A_{\omega}^{p_{1}}\odot A_{\nu}^{p_{2}}$, where $1<q,p_{1},p_{2}<\infty$ such that $q^{-1}=p_{1}^{-1}+p_{2}^{-1}$ and $\widetilde{\eta}^{\frac{1}{q}}\asymp\widetilde{\omega}^{\frac{1}{p_{1}}}\widetilde{\nu}^{\frac{1}{p_{2}}}$. Here $\widetilde{\tau}(r)=\int_r^1\tau(t)\,dt/(1-t)$ for all $0\le r<1$

Holocene sediment source analysis and paleoclimatic significance of core KZK01 from the eastern part of the Beibu Gulf

Identifying the sources of sediments is of great significance in reconstructing Holocene paleoclimate evolution in the Beibu Gulf and in understanding the characteristics of regional responses to changes in global climate. The Holocene paleoclimatic evolutionary history of the Beibu Gulf was investigated by chronological, geochemical, and mineralogical means using the sediments of Core KZK01 from the eastern part of the Beibu Gulf. The rare earth element (REE) distribution curves, (Gd/Yb)N and (La/Yb)N discriminant diagram, and (Gd/Lu)N and ∑LREE/∑HREE discriminant diagram indicated that the detrital materials in the eastern part of the Beibu Gulf primarily originated from Hainan Island and its proximal sources, with considerable contributions from Taiwan and Pearl River materials. Source analysis of clay minerals showed that Luzon Island was the main source of smectite, followed by Hainan Island. Rivers in Taiwan were the main sources of illite in the study area, followed by the Red River. The Red River was the main contributor of chlorite, followed by the Pearl River. Kaolinite mainly originated from Hainan Island and Guangxi. Coastal currents, surface currents, and warm currents were the main drivers of material transport. Paleoclimatic variations since the Holocene in the Beibu Gulf were divided into three stages: 12–9 cal kyr BP, 9–1.3 cal kyr BP, and 1.3 cal kyr BP to the present. During different stages of climatic evolution, drought was often accompanied by cold and humidity coexisted with warmth, and cold-dry-warm-humid alternation is characterized by significant phases. The illite crystallinity clearly recorded the extreme cold events, such as Bond Events (except Bond6) and the Younger Dryas, and the change trend was essentially consistent with the regional climate record, reflecting the control of global climate change on the process of land–sea interaction in the tropical region. Furthermore, it highlights the great potential of illite crystallinity as a proxy indicator for reconstructing the surface chemical weathering processes of the region

6G Network AI Architecture for Everyone-Centric Customized Services

Mobile communication standards were developed for enhancing transmission and network performance by using more radio resources and improving spectrum and energy efficiency. How to effectively address diverse user requirements and guarantee everyone's Quality of Experience (QoE) remains an open problem. The Sixth Generation (6G) mobile systems will solve this problem by utilizing heterogenous network resources and pervasive intelligence to support everyone-centric customized services anywhere and anytime. In this article, we first coin the concept of Service Requirement Zone (SRZ) on the user side to characterize and visualize the integrated service requirements and preferences of specific tasks of individual users. On the system side, we further introduce the concept of User Satisfaction Ratio (USR) to evaluate the system's overall service ability of satisfying a variety of tasks with different SRZs. Then, we propose a network Artificial Intelligence (AI) architecture with integrated network resources and pervasive AI capabilities for supporting customized services with guaranteed QoEs. Finally, extensive simulations show that the proposed network AI architecture can consistently offer a higher USR performance than the cloud AI and edge AI architectures with respect to different task scheduling algorithms, random service requirements, and dynamic network conditions

NtGNL1 Plays an Essential Role in Pollen Tube Tip Growth and Orientation Likely via Regulation of Post-Golgi Trafficking

Background: Tobacco GNOM LIKE 1 (NtGNL1), a new member of the Big/GBF family, is characterized by a sec 7 domain. Thus, we proposed that NtGNL1 may function in regulating pollen tube growth for vesicle trafficking. Methodology/Principal Findings: To test this hypothesis, we used an RNAi technique to down-regulate NtGNL1 expression and found that pollen tube growth and orientation were clearly inhibited. Cytological observations revealed that both timing and behavior of endocytosis was disrupted, and endosome trafficking to prevacuolar compartments (PVC) or multivesicular bodies (MVB) was altered in pollen tube tips. Moreover, NtGNL1 seemed to partially overlap with Golgi bodies, but clearly colocalized with putative late endosome compartments. We also observed that in such pollen tubes, the Golgi apparatus disassembled and fused with the endoplasmic reticulum, indicating abnormal post-Golgi trafficking. During this process, actin organization was also remodeled. Conclusions/Significance: Thus, we revealed that NtGNL1 is essential for pollen tube growth and orientation and it likel

Composition Semigroups on Weighted Bergman Spaces Induced by Doubling Weights

We prove that composition semigroups are strongly continuous on weighted Bergman spaces with doubling weights. Point spectra and compact resolvent operators of infinitesimal generators of composition semigroups are characterized

Effect of Autophagy Regulated by Sirt1/FoxO1 Pathway on the Release of Factors Promoting Thrombosis from Vascular Endothelial Cells

Factors promoting thrombosis such as von Willebrand factor (vWF) and P-selectin are essential for the development of atherosclerosis (AS) and arterial thrombosis. The processing, maturation and release of vWF are regulated by autophagy of vascular endothelial cells. The Sirt1/FoxO1 pathway is an important pathway to regulate autophagy of endothelial cells, therefore the Sirt1/FoxO1 pathway may be an important target for the prevention of thrombosis. We investigated the role of ox-LDL in the release of vWF and P-selectin and the expression of Sirt1 and FoxO1 by Western Blot, Flow Cytometry, ELISA, and tandem fluorescent mRFP-GFP-LC3. We found that vWF and P-selectin secretion increased and Sirt1/FoxO1 pathway was depressed in human umbilical vein endothelial cells (HUVEC) when treated with ox-LDL. Moreover, the expression of autophagy-related protein LC3-II/I and p62 increased. Then, we explored the relationship between autophagy regulated by the Sirt1/FoxO1 pathway and the secretion of vWF and P-selectin. We found that Sirt1/FoxO1, activated by the Sirt1 activators resveratrol (RSV) and SRT1720, decreased the secretion of vWF and P-selectin, which can be abolished by the autophagy inhibitor 3-MA. The expression of Rab7 increased when Sirt1/FoxO1 pathway was activated, and the accumulation of p62 was decreased. Autophagy flux was inhibited by ox-LDL and Sirt1/FoxO1 pathway might enhance autophagy flux through the promotion of the Rab7 expression. Taken together, our data suggest that by enhancing autophagy flux and decreasing the release of vWF and P-selectin, the Sirt1/FoxO1 pathway may be a promising target to prevent AS and arterial thrombosis