L~p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_（0,0） ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ < ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 < p < ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.     

PREDUAL SPACES FOR Q SPACES

To find the predual spaces Pα（R^n） of Qα（R^n） is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα（Rn） is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderon-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα（Rn）.     

用分布核空间刻画象征空间OpS_(1,1)~m

在五十年代,人们就建立了象征与分布核的形式上的联系;但这之后象征学派和 Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ学派一直处于分立的状态．即使对于 ＯＰＳ１,１ｍ,也只是对于它的一个子空间给出了刻画,这里用分布核空间刻画象征空间ＯｐＳ１,１ｍ     

象征算子的紧算子逼近算法和逼近速度

传统的微分方程的方法是利用Taylor展开用主象征逼近象征;本文用充分好的紧算子来逼近象征算子,并且逼近算子在算子范数意义下快速逼近原来的算子.     

A note on convolution-type Calderón-Zygmund operators

For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q （1 〈 p,q 〈 ∞） and on a party of endpoint spaces FO,q （1 ≤ q ≤ 2）, hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q （2 〈 q ≤ ∞）. In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q （2 〈 q ≤ ∞） under an integrable condition which approaches HSrmander condition infinitely.     

NEW WAVELET BASES FOR NON-HOMOGENEOUS SYMBOLIC SPACE OpSm1,1 AND RELATED KERNEL-DISTRIBUTION SPACES

This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.     

用小波限制紧算子逼近奇异积分算子的速度

根据Beylin-Coifman-Rokhlin和Yang的观点，用合适的小波基可以刻画性地研究C.Z算子或拟微分算子，这样就可以用小波来计算算子，比如可以从奇异积分算子的B-C-R算法刻画出发，用小波限制紧算子进行逼近，本文旨在计算作为原算子与逼近算子的差的误差算子的H1到L1的连续性范数的最佳衰减速度和在Lp上的连续性范数的衰减速度的范围。     

用分布核空间刻画象征空间OpS_(1,1)~m

在五十年代,人们就建立了象征与分布核的形式上的联系;但这之后象征学派和 Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ学派一直处于分立的状态．即使对于 ＯＰＳ１,１ｍ,也只是对于它的一个子空间给出了刻画,这里用分布核空间刻画象征空间ＯｐＳ１,１ｍ     

CHARACTERIZATION OF MULTIPLIER SPACES WITH DAUBECHIES WAVELETS

We characterize the multiplier spaces from Sobolev spaces to L2 with Daubechies wavelets without using capacity.     

用分布核空间刻画象征空间OpSm1

在五十年代，人们就建立了象征与分布核的形式上的联系；但这之后象征学派和Calderon-Zygmund学派一直处于分立的状态.即使对于OpSm1,1，也只是对于它的一个子空间给出了刻画，这里用分布核空间刻画象征空间OpSm11