Cn中多圆柱上广义Bloch空间的点乘子

讨论了Cn(n>1)中多圆柱上广义Bloch空间βp上的点乘子,根据p、q的不同情况得到βp空间到βq空间所有的点乘子,得到(1)当p<1时M(βp)=βp;(2)当p≥1时M(βp)=c;(3)当p>q时M(βp,βq)={0};(4)当p<q<1时M(βp,βq)=βq;(5)当p<1≤q时M(βp,βq)=Jp,q∩βq;(6)当1≤p<q时M(βp,βq)=c.     

A note on operator‐valued Fourier multipliers on Besov spaces

Let X be a Banach space. We show that each m : ? \ {0} → L (X ) satisfying the Mikhlin condition sup_{x ≠0}(‖m (x )‖ + ‖xm ′(x )‖) < ∞ defines a Fourier multiplier on B ^s _p,q (?; X ) if and only if 1 < p < ∞ and X is isomorphic to a Hilbert space; each bounded measurable function m : ? → L (X ) having a uniformly bounded variation on dyadic intervals defines a Fourier multiplier on B ^s _p,q (?; X ) if and only if 1 < p < ∞ and X is a UMD space. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类无穷矩阵代数的乘法序列连续性

设λ，μ是两个序列空间并有符号弱滑脊性，（λ，μ）是变换λ进入μ的无穷矩阵算子所成的无穷矩阵代数，本文研究了这类代数的强，Mackey、弱乘法序列连续性问题。     

Spherical convolution operators in spaces of variable Hölder order

In this paper, we study the images of operators of the type of spherical potential of complex order and of spherical convolutions with kernels depending on the inner product and having a spherical harmonic multiplier with a given asymptotics at infinity. Using theorems on the action of these operators in Hölder-variable spaces, we construct isomorphisms of these spaces. In Hölder spaces of variable order, we study the action of spherical potentials with singularities at the poles of the sphere. Using stereographic projection, we obtain similar isomorphisms of Hö lder-variable spaces with respect to n-dimensional Euclidean space (in the case of its one-point compactification) with some power weights.     

COEFFICIENT MULTIPLIERS ON MIXED NORM SPACES

§1　IntroductionSuppose thatf is analytic in the open unit disc D in the complex plane.We defineMp(r,f) =12π∫2π0 | f(reiθ) | pdθ1 / p,0

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Solving certain singly constrained convex optimization problems in production planning

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SOME MULTIPLIER THEOREMS FOR ANISOTROPIC HARDY SPACES ——In Memory of Professor Yongsheng Sun

Let A be a symmetric expansive matrix and Hp(Rn) be the anisotropic Hardy space associated with A. For a function m in L∞(Rn), an appropriately chosen function η in Cc∞(Rn) and j ∈ Z define mj(ξ) = m(Ajξ)η(ξ). The authors show that if 0 ＜ p ＜ 1 and (m)j belongs to the anisotropic nonhomogeneous Herz space K11/p-1,p(Rn), then m is a Fourier multiplier from Hp(Rn) to Lp(Rn). For p = 1, a similar result is obtained if the space K10,1(Rn) is replaced by a slightly smaller space K(w).Moreover, the authors show that if 0 ＜ p ≤ 1 and if the sequence {(mj)V} belongs to a certain mixednorm space, depending on p, then m is also a Fourier multiplier from Hp(Rn) to Lp(Rn).