BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f )is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H~2(Ω) of other pseudoconvex domains.In these arguments,Amar's L~p-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H~p(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THEω-TYPE CALDER′ON-ZYGMUND OPERATOR ON LORENTZ SPACE

In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).

A DERIVATIVE-HILBERT OPERATOR ACTING ON HARDY SPACES

Letμbe a positive Borel measure on the interval[0,1).The Hankel matrixHμ=(μn,k)n,k≥0 with entries μn,k=μn+k,whereμn=∫[0,1)tndμ(t),induces formally the operator asDHμ(f)(z)=∞∑n=0(∞∑k=0 μn,kak)z^(n),z∈D,where f(z)=∞∑n=0a_(n)z^(n) is an analytic function in D.We characterize the positive Borel measures on[0,1)such thatDHμ(f)(z)=f[0,1)f(t)/(1-tz)^(2)dμ(t) for all f in the Hardy spaces Hp(0<p<∞),and among these we describe those for which is a bounded(resp.,compact)operator from Hp(0<p<∞)into Hq(q>p and q≥1).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).

BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES

In this paper,we study band-dominated operators on Bergman-type spaces and prove that the C*-algebra of band-dominated operators is equal to the essential commutant of Toeplitz operators with a symbol in the set of bounded vanishing Lipschitz functions.On the Bergman space and the Fock space,we show that the C*-algebra of band-dominated operators equals the Toeplitz algebra.

Development of Operational Space Weather Prediction Models

In this report, we summarize the needs of space weather models, and recommend that developing operational prediction models, rather than transitioning from research to operation, is a more feasible and critical way for space weather services in the near future. Operational models for solar wind speed, geomagnetic indices, magnetopause, plasma sheet energetic electrons, inner boundary of ion plasma sheet, energetic electrons in outer radiation belt, and thermospheric density at low Earth orbit, have been developed and will be introduced briefly here. Their applications made a big progress in space weather services during the past two years in China.

q–differ-integral operator on p–valent functions associated with operator on Hilbert space

Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.

Active Compliance Control of a Position‑Controlled Industrial Robot for Simulating Space Operations

An industrial robot with a six-axis force/torque sensor is usually used to produce a zero-gravity environment for testing space robotic operations.However,using traditional force control methods,such as admittance control,causes position-controlled industrial robots to undergo from force divergence owing to intrinsic time delay.In this paper,a new force control method is proposed to eliminate the force divergence.A hardware-in-the-loop(HIL)simulator with an industrial robot is first presented.The free-floating satellite dynamics and the motion mapping from the satellites to simulator are both established.Thus,the effects of measurement delay and dynamic response delay on contact velocity and force are investigated.After that,a real-time estimation method for contact stiffness and damping is proposed based on the adaptive Kalman filter.The measurement delay is compensated by a phase lead model.Moreover,the identified contact parameters are adopted to modify contact forces,and thus the dynamics response delay can be compensated for.Finally,a co-simulation and experiments were conducted to verify the force control method.The results show that contact stiffness and damping could be identified exactly and that the simulation divergence could be prevented.This paper proposes an active compliance control method that can deal with force constrained tasks of a position-controlled robot in unknown environments.

SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES

We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.

LSTM-based lane change prediction using Waymo open motion dataset: The role of vehicle operating space

Lane change prediction is critical for crash avoidance but challenging as it requires the understanding of the instantaneous driving environment.With cutting-edge artificial intelligence and sensing technologies,autonomous vehicles(AVs)are expected to have exceptional perception systems to capture instantaneously their driving environments for predicting lane changes.By exploring the Waymo open motion dataset,this study proposes a framework to explore autonomous driving data and investigate lane change behaviors.In the framework,this study develops a Long Short-Term Memory(LSTM)model to predict lane changing behaviors.The concept of Vehicle Operating Space(VOS)is introduced to quantify a vehicle's instantaneous driving environment as an important indicator used to predict vehicle lane changes.To examine the robustness of the model,a series of sensitivity analysis are conducted by varying the feature selection,prediction horizon,and training data balancing ratios.The test results show that including VOS into modeling can speed up the loss decay in the training process and lead to higher accuracy and recall for predicting lane-change behaviors.This study offers an example along with a methodological framework for transportation researchers to use emerging autonomous driving data to investigate driving behaviors and traffic environments.

Analysis on EAST LHCD Operation Space by Using Simple Core-SOL-Divertor Model

A simple core-SOL-divertor model （CSD model） was developed to investigate qual- itatively the overall features of the operational space for the integrated core and edge plasma. In the CSD model, the core plasma model of ITER physics guidelines and the two-point SOL-divertor model are applied, This CSD model is validated by the two dimensional divertor transport code （B2-EIRINE） and by the JT-60U divertor recycling database, and this model is applicable to the low- and high-recycling state of the divertor plasma. The CSD model is applied to the study of the EAST operational space with lower hybrid current drive under various kinds of trade-off for the basic plasma parameters, and the relationship between the operational space and the plasma discharge duration is also discussed.

Monotonic Vector Space Model (Ⅰ): Concepts and Operations

Monotonic vector space (MVS), as a novel model in which there exist some monotonic mappings, is proposed. MVS model is an abstract of many practical problems (such as image processing, system capability engineering, etc.) and includes many useful important operations. This paper, as the first one of series papers, discusses the MVS framework, relative important concepts and important operations including partition, synthesis, screening, sampling, etc. And algorithms for these operations are the focus of this paper. The application of these operations in system capability engineering will be dealt with in the second part of this series of papers.

EXTENDED CESRO OPERATORS ON THE BLOCH SPACE IN THE UNIT BALL OF C^n

The paper defines an extended Cesaro operator Tg with holomorphic symbol g in the unit ball B of Cn asWhere is the radial derivative of g. In this paper, the author characterizes g for which Tg is bounded (or compact) on the Bloch space B and the little Bloch space Bo-

Boundedness of Hausdorff operators on some product Hardy type spaces

We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

Let p 〉 0 and μ be a normal function on [0, 1）, u（r） = （1 - r2）1＋n^pμ（r） for r ∈ [0, 1）. In this article, the bounded or compact weighted composition operator Tφ,ψ from the μ-Bergman space AP（p） to the normal weight Bloch type space β （r）in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator Cφ is compact from A^p（μ） to βv, is given. At the same time, the authors give the briefly sufficient and necessary condition that Cv is compact on βμ, for a 〉 1.

Spatial Operator Algebra for Free-floating Space Robot Modeling and Simulation

As the dynamic equations of space robots are highly nonlinear,strongly coupled and nonholonomic constrained,the efficiency of current dynamic modeling algorithms is difficult to meet the requirements of real-time simulation.This paper combines an efficient spatial operator algebra（SOA） algorithm for base fixed robots with the conservation of linear and angular momentum theory to establish dynamic equations for the free-floating space robot,and analyzes the influence to the base body＇s position and posture when the manipulator is capturing a target.The recursive Newton-Euler kinematic equations on screw form for the space robot are derived,and the techniques of the sequential filtering and smoothing methods in optimal estimation theory are used to derive an innovation factorization and inverse of the generalized mass matrix which immediately achieve high computational efficiency.The high efficient SOA algorithm is spatially recursive and has a simple math expression and a clear physical understanding,and its computational complexity grows only linearly with the number of degrees of freedom.Finally,a space robot with three degrees of freedom manipulator is simulated in Matematica 6.0.Compared with ADAMS,the simulation reveals that the SOA algorithm is much more efficient to solve the forward and inverse dynamic problems.As a result,the requirements of real-time simulation for dynamics of free-floating space robot are solved and a new analytic modeling system is established for free-floating space robot.

COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL

We find a lower bound for the essential norm of the difference of two composition operators acting on H 2（BN ） or As2 （BN ） （s 1）. This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.

INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).

COMPOSITION OPERATOR ON BERS-TYPE SPACES

Necessary and sufficient conditions are established for a composition operator C(phi)f = f o phi to be bounded or compact on the Bers-type space H-alpha(infinity) and the little Bers-type space H-alpha(infinity). The boundedness and compactness of the composition operator C-phi on A(infinity)(phi) are characterized, which generalize the case of C-phi on H-alpha(infinity).

Multilinear Calder′on Zygmund operators on variableexponent Morrey spaces over domains

The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.