Multilinear transference of Fourier and Schur multipliers acting on noncommutative -spaces
نویسندگان
چکیده
Abstract Let G be a locally compact unimodular group, and let $\phi $ some function of n variables on . To such , one can associate multilinear Fourier multiplier, which acts -fold product the noncommutative $L_p$ -spaces group von Neumann algebra. One may also define an associated Schur Schatten classes $S_p(L_2(G))$ We generalize well-known transference results from linear case to case. In particular, we show that so-called “multiplicatively bounded $(p_1,\ldots ,p_n)$ -norm” multiplier is above by corresponding multiplicatively norm with equality whenever amenable. Furthermore, prove bilinear Hilbert transform not as vector-valued map $L_{p_1}(\mathbb {R}, S_{p_1}) \times L_{p_2}(\mathbb S_{p_2}) \rightarrow L_{1}(\mathbb S_{1})$ $p_1$ $p_2$ are $\frac {1}{p_1} + \frac {1}{p_2} = 1$ A similar result holds for certain Calderón–Zygmund-type operators. This in contrast nonvector-valued Euclidean
منابع مشابه
Multilinear Fourier Multipliers with Minimal Sobolev Regularity
Letm be a positive integer. In this talk, we will introduce optimal conditions,expressed in terms of Sobolev spaces, on m-linear Fourier multiplier operatorsto be bounded from a product of Lebesgue or Hardy spaces to Lebesgue spaces.Our results are sharp and cover the bilinear case (m = 2) obtained by Miyachiand Tomita [1]. References[1] Miyachi A., and Tomita N., Minima...
متن کاملMaximal Transference and Summability of Multilinear Fourier Series
We obtain a maximal transference theorem that relates almost everywhere convergence of multilinear Fourier series to boundedness of maximal multilinear operators. We use this and other recent results on transference and multilinear operators to deduce Lp and almost everywhere summability of certain m-linear Fourier series. We formulate conditions for the convergence of multilinear series and we...
متن کاملCommutators for Fourier multipliers on Besov Spaces
The mapping properties of commutators [T,M ] = TM −MT , for operators between function spaces, and their various generalizations play an important role in harmonic analysis, PDE, interpolation theory and other related areas. A typical situation arises when M = Mb is the pointwise multiplication by a function b and T is a Calderón–Zygmund operator on R. Then well– known results of A.P. Calderón ...
متن کاملFourier Multipliers on Weighted L-spaces
In his 1986 paper in the Rev. Mat. Iberoamericana, A. Carbery proved that a singular integral operator is of weak type (p, p) on Lp(Rn) if its lacunary pieces satisfy a certain regularity condition. In this paper we prove that Carbery’s result is sharp in a certain sense. We also obtain a weighted analogue of Carbery’s result. Some applications of our results are also given.
متن کاملAbel-schur Multipliers on Banach Spaces of Infinite Matrices
We consider a more general class than the class of Schur multipliers namely the Abel-Schur multipliers, which in turn coincide with the bounded linear operators on `2 preserving the diagonals. We extend to the matrix framework Theorem 2.4 (a) of a paper of Anderson, Clunie, and Pommerenke published in 1974, and as an application of this theorem we obtain a new proof of the necessity of an old t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2022
ISSN: ['1496-4279', '0008-414X']
DOI: https://doi.org/10.4153/s0008414x2200058x