Mihlin multiplier theorem
Web29 nov. 2016 · We prove that the existence of a Mihlin-Hörmander functional calculus for an operator L implies the boundedness on L^p of both the maximal multiplier operators and the continuous square functions build on spectral multipliers of L. The considered multiplier functions are finitely smooth and satisfy an integral condition at infinity. Web27 jun. 2024 · for 0 ≤ j ≤ k and k > d / 2. Or more generally. where χ is a non-zero smooth cut-off function of compact support which vanishes near the origin and ‖ f ‖ H s = ‖ ( 1 + ⋅ 2) s / 2 f ^ ‖ L 2. Then Fourier-multiplier operator T f ^ = m ( ξ 2) f ^ is bounded on L p ( R d) for 1 < p < ∞. Why condition (1) implies (2) in the ...
Mihlin multiplier theorem
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<∞,Theorem 1.1 recovers the Lp(G)-H¨ormander Mihlin theorem in [16]. Remark 1.3. The H¨ormander-Mihlin theorem has been extended by several authors to spectral multipliers of Laplacian and sub-Laplacians, and settings that go beyond the Euclidean case. The literature is so broad that it is impossible to provide complete ...
Web25 nov. 2024 · Assumption (ii) in Theorem 1.2 is a Fourier multiplier condition, whereas the corresponding assumption in Stein interpolation for the complex interpolation method can be seen as a pointwise multiplier condition. Web16 jul. 2024 · The Mikhlin multiplier states the following: Let m: R n ∖ { 0 } → C satisfy the following: ∂ α m ( ξ) ≤ C 0 ξ − α , ∀ α ∈ N 0 n i.e. alpha is a multi-index with α ≤ n + 2. Then, for all 1 < p < ∞, ∃ B = B ( m, n, p) > 0 such that T m f L p ≤ B f L p, ∀ f …
Web米赫林乘子定理(Mihlin multiplier theorem)是给出函数成为Lp(p>1)乘子的充分条件的定理。 中文名 米赫林乘子定理 外文名 Mihlin multiplier theorem 适用范围 数理科学 相关视频 查看全部 目录 1简介 2具体内容 3乘子 米赫林乘子定理简介 编辑播报 米赫林乘子定理是给出函数成为Lp(p>1)乘子的充分条件的定理。 米赫林乘子定理具体内容 编辑播报 米赫林乘子定 … WebAs an application of our theorem we deal with the Hörmander-Mihlin type multiplier theorem for the Hankel transform. Let µ ≥−1/2andφ ∈ L∞(0,∞). We define a Hankel multiplier operator Mµ φ with multiplier φ by Mµ φ f = Hµ(φHµ(f)) for f ∈ L2(0,∞).SinceHµ is an isometry on L2(0,∞), the multiplier operator Mµ φ is
Web8 nov. 2014 · Our main result is a Hörmander–Mihlin multiplier theorem for finite-dimensional cocycles with optimal smoothness condition. We also find …
Webcase where the multiplier has sufficiently many bounded derivatives ([10] Theorem 20) where the H¨ormander-Mihlin theorem can be applied locally. We note that this result is not applicable to the multipliers eit ξ α. Our main result is that the unimodular multipliers discussed above are bounded on all modulation spaces. Theorem 1. hungarian thank youWeb13 jan. 2024 · Subsequent generalisations to Mihlin's theorem were done by Hörmander [34], Calderón and Torchinsky in [4], Taibleson and Weiss [49], Baernstein and Sawyer [3], Seeger [45,46,47] and many others. hungarian themeWebAn operator–valued Mikhlin theorem is proved for multipliers of the form M : ℝn → ℒ (X, Y) where X and Y are UMD spaces. The usual norm bounds of the classical Mikhlin condition are ... castelli men's sella rain jacketWebFourier multiplier theorems in this article to study the H∞-calculus for generators of C0-groups. Other potential applications could be given to the theory of dispersive equations. For instance the classical Strichartz estimates can be viewed as operator-valued Lp-Lq-multiplier theorems. Here the multipliers are often not smooth, as is the ... hungarian to nzdWebHo¨rmander-Mihlin-Marcinkiewicz condition. In our analysis, we use the difference structure of the unitary dual of a compact Lie group. Our results cover the sharp Ho¨rmander … castello kensingtonWebH ormander’s multiplier theorem [H or60] for 1 hungarian tilesWeb11 mrt. 2010 · the vector-valued multiplier theorem 2555 2. Different Mihlin conditions Following the approach in [6], rather than the classical Mihlin multiplier condi tion, it will … castelli puffy jacket test