Q_p空间中K-泛函与光滑模等价性

<正>1引言令g(·,w)为复平面单位圆盘D(|z|1)上极点在W的Green函数g(z,w)=-log|φ_w(z)|,z,w∈D,其中φ_w为从D到其上的M(o|¨)bius变换φ_w(z)=(w-z)/(1-wz).记H(D)为D上全纯函数全体,dm(z)为Lebesgue测度.称函数f属于Q_p空间(0≤P∞)是指f(z)∈H(D)且满足||f||_(Q_p)~2:=supw∈D∫_D|f'(z)|~2g~p(z,w)dm(z)+∞.易知~([1]),||·||_(Q_p)为半模.若取模为|f(0)|+||f||_(Q_p),则Q_p空间为Banach空间,且有     

单位圆盘上全纯映照模的精细Schwarz引理北大核心CSCD

记DC为单位圆盘,B^p={z∈C^n:n∑i=1|z_i|~p<1},1相似文献   

关于单叶从属函数的一个系数不等式

<正> §1.引言 记■={z||z|<1}.设F(z)■是■上的解析函数.函数w=F(z)将映成区域S_F.设f(z)在中解析,如果w=f(z)的一切值都落在S_F上,那么说f(z)从属于F(z).记为f(z)相似文献   

关于Bernstein-Kantorovi多项式在L_P[0,1]空间中的逼近阶

§1.引 言 对于1≤p<∞,以L_p[a,b]表示适合||f||L_p[a,b]={ |f(x)|~pdx}~(1/p)<∞的f全体。记L_∞[a,b]≡C[a,b],||f||L_∞[a,b]=max|f(x)|. 若a=0.b=1,简记||f||L_p[0,1]=||f||L_p·又设 B_p={g:g(x),g’(x),x(1一x)g’(x)∈L_p[0、1]; x(1-x)g’(x)|x=0,1=0},     

Use Cesro Means To Describe Two Classes of Functions

Let H(D)be the collection of functions which are analytic in the unitdisc D.we call B_0={f∈H(D),(?)(1-|z|~2)|f’(z)|=0}litlle Bloch space.Letf∈H(D),0相似文献   

关于corona(日冕)问题

设Δ={|z|<1},H~∞(Δ)表示Δ上一切有界解析函数全体所组成的函数族.它是一个Banach代数,因若f和g∈H~∞ (Δ),则fg∈H~∞(Δ),且||fg||_∞≤||f||_∞·||g||_∞.设对单位圆内任何一点z,令M_z={f∈H~∞(Δ):f(z)=0},则M_z是H~∞ (Δ)的一个极大理想.设 表示 H~∞(Δ)的极大理想空间,则它在弱拓扑下成为一个紧致的Hausdorff空间.若对z,|z|<1,则点赋值     

圆内解析函数的某些性质

<正> 若函数 f(z)是圆|z|<1内的解析函数,且满足:(?)则称函数 f(z)属于 H_p 类,简记为 f(z)∈H_p.同样若函数 u(z)在圆|z|<1内调和,且满足上述条件,则称函数 u(z)属于 h_v 类,     

Bloch型空间上广义Cesàro算子的本性模(英文)

The Bloch-type space Bω consists of all functions f ∈ H(B) for which||f||Bω=sup/z∈Bω(z)|▽f(z)|< ∞.Let T be the extended Ces`aro operator with holomorphic symbol . The essential norm of T as an operator from Bω to Bμ is denoted by ||T||e,B ω→Bμ . The purpose of this paper is to prove that, for ω, μ normal and ∈H(B)||T||e,B ω→Bμ■ lim sup|z|→1 μ(z)|■ (z)|∫ |z| 0 dt ω(t) .     

A Note on a Paper of Dickmeis etc

Let X be a Banach space, X~* be the class of all bounded and sublinear functionals T on X, i .e. (1) |T(f+g)|≤|T f|+|Tg|for all f, gX; (2) |T(af)|=|a||Tf|for all numbers a and f X; (3) ‖T‖_x~·=sup |T f|<∞. In[1] , W.Dickmeis, R.J.Nessel and E. van Wickeren proved the following theorem.     

平移不变空间的非均匀采样

为了从采样值稳定和惟一地重建信号f(x),函数在采样集{xj,j=∈Z}上的采样值{f(xj),j∈Z}要满足A||f||L^p^p≤∑j∈Z|f(xj)|^p≤B||f||L^p^p.本文研究在平移不变空间V^p[φ]中使上式成立的条件,在几种情况下,得到了使上式成立的采样条件,并建立了由采样值重建f(x)的重建算法,该算法比一般的迭代重建算法收敛更快．     

GENERALIZED HILBERT OPERATOR AND FEJR-RIESZ TYPE INEQUALITIES ON THE POLYDISC

Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) = ∞ |k|=0 i1,···,in≥0 ai1,···,in n j=1 Γ(γj + kj + 1)Γ(kj + ij + 1) Γ(kj + 1)Γ(kj + ij + γj + 2) zk,where γ∈ Cn, such that R γj > -1, j = 1, 2, , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type inequalit...     

一族解析函數的模數

<正> §1.設函數f(ζ)在單位圓|ζ|<1中是正則的,f(0)=0,當|ζ_1|<1,|ζ_2|<1時f(ζ_1)·f(ζ_2)≠1.這種函數的全體記做C.首先研究這種函數的是比巴霸赫,其後有愛倫貝格.洛各淨司基證明:對於C中任一函數f(ζ),必從屬於C中某一單葉函數g(ζ).     

ON SATURATION CLASS FOR JACKSON SUMS OF BESSEL SERIES

Let function f(z) be analytic in |z|<1 and continuous on |z|≤1. The saturation class for the Jackson sums of the Bessel series of f(z) is discussed.     

單葉函數的係數(Ⅲ)

<正> 記在單位圓|z|<1中正則單葉的函數的全體為S.開於|c_n|的估計,目前最好的是巴西列維奇所證明的     

Maximal inequalities for a continuous semimartingale

Let X =( X t ) t S 0 be a continuous semimartingale given by d X t = f ( t ) w ( X t )d d M ¢ t + f ( t ) σ ( X t )d M t , X 0 =0, where M =( M t , F t ) t S 0 is a continuous local martingale starting at zero with quadratic variation d M ¢ and f ( t ) is a positive, bounded continuous function on [0, X ), and w , σ both are continuous on R and σ ( x )>0 if x p 0. Denote X 𝜏 * =sup 0 h t h 𝜏 | X t | and J t = Z 0 t f ( s ) } ( X s )d d M ¢ s ( t S 0) for a nonnegative continuous function } . If w ( x ) h 0 ( x S 0) and K 1 | x | n σ 2 ( x ) h | w ( x )| h K 2 | x | n σ 2 ( x ) ( x ] R , n >0) with two fixed constants K 2 S K 1 >0, then under suitable conditions for } we show that the maximal inequalities c p , n log 1 n +1 (1+ J 𝜏 ) p h Á X 𝜏 * Á p h C p , n log 1 n +1 (1+ J 𝜏 ) p (0< p < n +1) hold for all stopping times 𝜏 .     

BMO ESTIMATES FOR MULTILINEAR FRACTIONAL INTEGRALS

In this paper,the authors prove that the multilinear fractional integral operator T A 1,A 2 ,α and the relevant maximal operator M A 1,A 2 ,α with rough kernel are both bounded from L p (1 p ∞) to L q and from L p to L n/(n α),∞ with power weight,respectively,where T A 1,A 2 ,α (f)(x)=R n R m 1 (A 1 ;x,y)R m 2 (A 2 ;x,y) | x y | n α +m 1 +m 2 2 (x y) f (y)dy and M A 1,A 2 ,α (f)(x)=sup r0 1 r n α +m 1 +m 2 2 | x y | r 2 ∏ i=1 R m i (A i ;x,y)(x y) f (y) | dy,and 0 α n, ∈ L s (S n 1) (s ≥ 1) is a homogeneous function of degree zero in R n,A i is a function defined on R n and R m i (A i ;x,y) denotes the m i t h remainder of Taylor series of A i at x about y.More precisely,R m i (A i ;x,y)=A i (x) ∑ | γ | m i 1 γ ! D γ A i (y)(x y) r,where D γ (A i) ∈ BMO(R n) for | γ |=m i 1(m i 1),i=1,2.     

典型實照的奇函數

<正> 1.設函數f(z)在單位圓|z|<1是正則的,f(0)=0,f’(0)=1;且在此單位圓內,當(z)≠0時,記此種典型實照函數的全體為T_r. 戈魯淨證明T_r中的函數f(z)在單位圓|z|<1內,可以用司帝皆積分     

开拓劳宾生和戈鲁辛的几个定理

<正> 1.设 p 次对称函数(?)在单位圆|z|<1中是正则的单叶的,此种函数的全体成一函数族 S_p.当p=1时,简讯 S_1为 S.设ω=f(z)∈S_p 映照|z|<1于 W 面上时,其像关于原点成星形,此种 f(z)成 S_p 之一子族S_p.设 f(z)∈S_p,     

On saturation class for Jackson sums of Bessel series

Let function f (z) be analytic in |z|＜1 and continuous on |z|≤1. The saturation class for the Jackson sums of the Bessel series of f(z) is discussed.     

Non-existence of Global Solutions for a Fractional Wave-diffusion Equations

We considered the Cauchy problem for the fractional wave-diffusion equation $$D^αu-Δ|u|^{m-1}u+(-Δ)^{β/2}D^γ|u|^{l-1}u=h(x,t)|u|^p+f(x,t)$$ with given initial data and where p > 1, 1 < α < 2, 0 < β < 2, 0 < γ < 1. Nonexistence results and necessary conditions for global existence are established by means of the test function method. This results extend previous works.