Notes on the Spaces of Bilinear Multipliers
نویسنده
چکیده
A locally integrable function m(ξ, η) defined on R × R is said to be a bilinear multiplier on R of type (p1, p2, p3) if Bm(f, g)(x) = Z
منابع مشابه
A homomorphism theorem for bilinear multipliers
In this paper we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of K. de Leeuw’s theorem for bilinear multipliers of strong and weak type. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding b...
متن کاملThe Marcinkiewicz Multiplier Condition for Bilinear Operators
This article is concerned with the question of whether Marcinkiewicz multipliers on R2n give rise to bilinear multipliers on R×R. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers f...
متن کاملMultilinear 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 کاملSome algebraic properties of Lambert Multipliers on $L^2$ spaces
In this paper, we determine the structure of the space of multipliers of the range of a composition operator $C_varphi$ that induces by the conditional expectation between two $L^p(Sigma)$ spaces.
متن کاملBilinear multipliers and transference
(defined for Schwarzt test functions f and g in ) extends to a bounded bilinear operator from Lp1 (R)×Lp2 (R) into Lp3 (R). The theory of these multipliers has been tremendously developed after the results proved by Lacey and Thiele (see [16, 18, 17]) which establish that m(ξ,ν) = sign(ξ +αν) is a (p1, p2)-multiplier for each triple (p1, p2, p3) such that 1 < p1, p2 ≤∞, p3 > 2/3, and each α∈R \...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009