Maximal operators of pseudo-differential operators with rough symbols

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb is bounded from H1（Rn） into L1（Rn） only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσ be the operators that its symbol is Sσ1,δ with 0 ≤δ〈 1, if b ∈ LMO∞, then, the commutator [b, Tσ] is bounded from H1（Rn） into L1（Rn） and from L∞（Rn） into BMO（Rn）; If [b,Tσ] is bounded from H1（Rn） into L1（Rn） or L1（Rn） into BMO（Rn）, then, b ∈ LMOtoc.

General Formulae for Two Pseudo-differential Operator

Some general formulas in the Sato theory related to the nonisospectral KP and mKP hierarchies are derived for simplifying calculations.

Pseudo-differential Operators and Generalized Lax Equations in Symbolic Computation

In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.

Boundedness for Multilinear Operators of Pseudo-Differential Operators

In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the Lp (1 p norm inequalities for the multilinear operators.

THE DESIGN OF HIGH PERFORMANCE LINEAR TRANSCONDUCTOR

An improved structure of linear transconductor is presented in this paper. It is analyzed in theory and simulated with Spectre based on 0.25μm CMOS process. The simulation results show that the differential input voltage of the proposed transconductor is 4.0Vpp(peak to peak), whereas the differential input voltage of the existing source degeneration structure is 2.2Vpp, when their nonlinear errors are required to be less than 0.15%.

Design and Analysis of a Power Efficient Linearly Tunable Cross-Coupled Transconductor Having Separate Bias Control

A common current source, generally used to bias cross-coupled differential amplifiers in a transconductor, controls third harmonic distortion (HD3) poorly. Separate current sources are shown to provide better control on HD3) . In this paper, a detailed design and analysis is presented for a transconductor made using this biasing technique. The transconductor, in addition, is made to offer high Gm, low power dissipation and is designed for linearly tunable Gm with current mode load as one of the applications. The circuit exhibits HD3) of less than –43.7 dB, high current efficiency of 1.18 V-1 and Gm of 390 μS at 1 VGp-p @ 50 MHz. UMC 0.18 μm CMOS process technology is used for simulation at supply voltage of 1.8 V.

考虑结电容和跨导非线性的辐射频段EMI分析模型

宽禁带WBG(wide band gap)半导体电力电子器件由于其开关频率高、开关速度快、寄生参数大等特点从噪声源头引发了越来越严峻的电磁干扰问题。然而,传统的噪声源研究主要集中在30 MHz传导频段以内,如何评估噪声源在30~300 MHz较高频率范围内的辐射频段产生的影响仍存在不确定性,因此提出1种改进的WBG器件电磁干扰分析模型,与传统的非对称梯形波电磁干扰模型相比,首次详细考虑了WBG器件的结电容和跨导体的非线性特性,评估了非线性参数对辐射频段噪声的影响,并进一步提出该模型在辐射频段噪声源抑制中的应用。仿真结果验证了所提计算方法的准确性,基于SiC器件的硬件测试结果与理论分析相吻合。

Pseudo-Differential Operators of Homogeneous Symbol Class Associated with the Weinstein Transform

In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on H_(α,2)^(r) are proven with the help of the Weinstein transform technique.

A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L_(2)^(a) (R_(+);m_(a)(x)dx)

Pseudo-differential operators(PDO)Q(x,L_(a,x))and Q(x,L_(a,x))involving the index Whittaker transform are defined.Estimates for these operators in Hilbert space L_(2)^(a)(R+;m_(a)(x)dx)are obtained.A symbol classΩis introduced.Later product and commutators for the PDO are investigated and their boundedness results are discussed.

GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION

The Landau equation is studied for hard potential with-2≤γ≤1.Under a perturbation setting,a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space H_(x)^(d)L_(v)^(2)(d>3/2),which extends the results of[11]in the torus domain to the whole space R_(x)^(3).Here we utilize the pseudo-differential calculus to derive our desired result.

Analysis and Design of a Quadrature Down-Conversion Mixer for UHF RFID Readers

A quadrature mixer with a shared transconductor stage is analyzed,including voltage conversion gain, linearity, noise figure, and image rejection. The analysis indicates it has better performance than a conventional Gilbert mixer pair in commutating mode. A quadrature down-conversion mixer based on this topology is designed and optimized for an ultra high frequency RFID reader. Operating in the 915MHz ISM band, the presented quadrature mixer measures a conversion gain of 12.5dB,an IIP3 of 10dBm, an IIP2 of 58dBm, and an SSB noise figure of 17.6riB. The chip was fabricated in a 0. 18μm 1P6M RF CMOS process and consumes only 3mA of current from a 1.8V power supply.

一种可调高线性度跨导器

本文提出了一种新的跨导器结构,它采用CMOS复合对管实现,可以通过调节栅极电压改变跨导器的跨导值,适合应用于高线性的连续时间滤波器.仿真结果表明,在供电电压为5伏,输人差分信号峰峰值为2.3伏的情况下,可以达到小于0.5％的总谐波失真.

基于低电源电压混频器的设计

提出了一种适用于低电源电压应用的混频器,其核心部分采用开关跨导形式,使得开关器件导通时的有限开态电阻引起的电压降减小到零,并在输出端采用折叠级联输出,降低了负载电阻引起的直流电压降,达到了在低电源电压下应用的目的.在1.3 V的电源电压下,电路仿真结果显示:转换增益为-11.5 dB,噪声系数为20.648 dBm,1 dB压缩点为-5.764 dBm,三阶交调失真点为4.807 dBm.

可调频率跨导电容Chebyshev滤波器的设计及仿真

首先提出了一种新的跨导运放,其输入级采用了工作在线性区的MOS管作源极负反馈有源电阻实现其良好的线性度,输出级采用折叠式结构,并在电路中引入电压共模负反馈(CMFB)稳定其静态工作点。接着提出了一种新的利用开关电容技术调节跨导运放偏置电流值大小的电路,应用该电路可以精确调节跨导运放Gm值的大小,应用这些电路设计得到了四阶Chebyshev低通滤波器,并实现其频率的精确可调,0.35μm2层多晶硅,4层金属CMOS工艺Spicemodel仿真结果表明设计正确、有效。

一种全集成的RSSI电路

基于0.18μm RF CMOS工艺,设计了一种全集成的接收信号强度指示计(RSSI)电路.该电路片内集成了限幅放大器,全波整流器,失调减法器,直流失调提取电路和输出缓冲器.该RSSI电路提供放大后的中频输出以及指示输入信号强度的RSSI电压输出.通过在直流失调提取电路中应用微电流偏置的跨导放大器,大幅减小了版图面积,提高了集成度,降低了成本.这种RSSI电路不仅适合低中频接收机,尤其适合于零中频应用.测试结果表明,电路实现了55dB的输入线性检测范围,同时占用版图面积为0.033mm2,功耗为3.1mA.

低功耗高线性多频带Gm-C低通滤波器

基于翻转电压跟随器(Flipped Voltage Follower,FVF)的拓扑结构,实现了一种低功耗高线性的跨导器,跨导值可由控制电压精确改变。运用此跨导单元设计了一种适用于无线收发机系统的多频带Gm-C低通滤波器。该滤波器是由双二次节级联构成的六阶巴特沃斯型滤波器,可实现70 k Hz,140 k Hz和210 k Hz多频带选择。采用SMIC 0.18μm CMOS工艺设计的滤波器的线性度IIP3大于22.6 d Bm,在1.8 V电源电压下消耗的功耗为1.37 m W。

CMOS宽带互导器及高Q值VHF选频电路

本文详细论述了一种可以有多输入的CMOS宽带互导（WBTC）电路，该电路具有线性，频率响应好的特点。利用该电路可以构成高Q值的VHF可调谐选频电路，文章中给出并详细分析了具体电路，最后是计算机仿真的结果。

改善跨导放大器线性化方法的研究

讨论了电流模式电路及跨导器的基本概念及性能特点,研究并给出了改善输入级传输特性的线性程度并扩大线性范围的方法。