Weil Multipliers

This paper studies a class of linear operators on spaces of functions of one real variable, which correspond to multiplication by a measurable function under the Weil transform These operators are called Weil multipliers, and arise out of the authors' study of Gabor series and radar ambiguity functions. Representation theory provides a natural class of Weil multipliers: the set of doubly periodic functions with absolutely convergent Fourier series, It will be proved that functions in are multipliers for all and, therefore, define bounded linear endomorphisms of Also, we record the fact that the Wiener lemma tells us something about the orbit structure of these multipliers acting on function spaces on the Heisenberg nilmanifold. Linear maps that correspond to multiplication by a function under a unitary conjugacy have a particularly simple spectral decomposition, which yields an approximation theory for these operators and provides insight into the foundation of the authors' previous work on approximate orthonormal bases. Finally, the problem of inversion of a multiplier will be analyzed for smooth functions that have a specified structure near their zeros.     

Almost-Periodic Multipliers

In this work we study the necessary and sufficient conditions for a generalized trigonometric series in order for it to be the series of a Stepanoff almost-periodic function fS ^q (R),1q<. We consider analogous conditions for functions belonging to D(,R). Finally, we characterize the multipliers of invariance of the (B ¹(),B ¹()) type.     

Multipliers on Besov spaces

It is proved in this paper that the characteristic function of the half-space is not a multiplier for the pair (B _pq ^1/p , B _p ^1/p ), 1<p<, 1<q . In addition, necessary and sufficient conditions are found for the validity of the inclusion.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 36–50, 1984.     

Multipliers of Fourier series

New statements are proved regarding multipliers of trigonometric Fourier series in the space C of continuous periodic functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1686–1693, December, 1991.     

Multipliers of Sobolev spaces

Let W^m,p denote the Sobolev space of functions on $\text{R}$ⁿ whose distributional derivatives of order up to m lie in L^p($\text{R}$ⁿ) for 1 ? p ? ∞. When 1 < p < ∞, it is known that the multipliers on W^m,p are the same as those on L^p. This result is true for p = 1 only if n = 1. For, we prove that the integrable distributions of order ?1 whose first order derivatives are also integrable of order ?1, belong to the class of multipliers on W^m,1 and there are such distributions which are not bounded measures. These distributions are also multipliers on L^p, for 1 < p < ∞. Moreover, they form exactly the multiplier space of a certain Segal algebra. We have also proved that the multipliers on W^m,l are necessarily integrable distributions of order ?1 or ?2 accordingly as m is odd or even. We have obtained the multipliers from L¹($\text{R}$ⁿ) into W^m,p, 1 ? p ? ∞, and the multiplier space of W^m,1 is realised as a dual space of certain continuous functions on $\text{R}$ⁿ which vanish at infinity.     

Multipliers in Hardy-Sobolev Spaces

For 1 < p < ∞ and 0 ≤ n − sp < 1, we give characterizations of the space of pointwise multipliers of the holomorphic Hardy-Sobolev spaces H_s^p on the unit ball B of As an application of these results we obtain a corona theorem for these spaces.     

Multipliers and Morrey Spaces

We study the pointwise multipliers from one Morrey space to another Morrey space. We give a necessary and sufficient condition to grant that the space of those multipliers is a Morrey space as well.     

Hardy空间的乘子

本文刻划了Hardy空间H^p（1≤p≤∞）到Bloch空间的乘子,推广了前人的结果。     

Multipliers of Schatten classes

Let C_p be the class of all compact operators A on the Hilbert space l² for which $\text{∑¦λ}{}_{\mathrm{i}}\text{¦}{}^{\mathrm{p}}\text{< ∞}$, where {λ_i} is the eigen values of $\text{(A}{}^1\text{A)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The object of this paper is to prove some results concerning the Schur multipliers of C_p.     

到序列空间的乘子

这篇论文刻画了 (Ap,α,lq) (0

0 ,p ≤ q≤∞ )的特征 ,作为其推论 ,获得了 (Al;lq)、(Hp,lq)、(Gp,lq)和 (Bp,lq) (0

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Dirichlet型空间上的乘子

本文主要根据τ与μ的不同取值分三种情况刻划了Cn中单位球上Dirichlet 型空间上的点乘子空间M(Dτ,Dμ),并通过两个函数的构造表明:当τ≤n时,包含 关系M(Dτ)(?)Dτ和当τ>μ,τ>n-1时,包含关系M(Dτ)(?) M(Dμ)是严格的.     

Multipliers on certain function spaces

Si generalizza un teorema di deLeeuw per moltiplicatiri su spazi di Lorentz e spazi con norme miste.

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Dedicated to my dear teacher, Professor Guido Weiss, for his 65 birthday