site stats

Hausdorff-young inequality

WebApr 15, 2024 · Sharp Hausdorff-Young inequality. The sharp Hausdorff-Young inequality plays an important role in Harmonic analysis. However, even for the two-sided quaternion Fourier transform, the sharp Hausdorff-Young inequalities has been overlooked for many years, which was only achieved recently by the symplectic decomposition of … WebHausdorff-Young theorem, and Young's inequality, where Fourier transforms and convolutions are used respectively. II* Diagram proof of the Hausdorίϊ-Young Theorem* As a corollary of the author's diagram proof [6] of Riesz's theorem, we 1 Terms used in the introduction will be defined in the paper. 97

(PDF) Vector-valued Hausdorff-Young inequality and applications

WebSep 17, 2024 · 1 The Hausdorff–Young inequality says that If f ∈ L p ( R d), 1 ≤ p ≤ 2 then ‖ f ^ ‖ L p ′ ( R) ≤ ‖ f ‖ L p ( R), 1 p + 1 p ′ = 1. where f ^ is the Fourier transform of f. I would … WebOct 26, 2024 · The Young inequalities and the Hausdorff–Young inequalities are two fundamental results in Fourier analysis. They have profound applications in analysis. For … chassis metal https://connersmachinery.com

Young’s inequalities and Hausdorff–Young inequalities on

WebMay 10, 2024 · The Hausdorff−Young inequality is a foundational result in the mathematical field of Fourier analysis. As a statement about Fourier series, it was discovered by William Henry Young ( 1913) and extended by Hausdorff ( 1923 ). It is now typically understood as a rather direct corollary of the Plancherel theorem, found in 1910, … WebJun 5, 2024 · Hausdorff-Young inequalities. Estimates of the Fourier coefficients of functions in $ L _ {p} $; established by W.H. Young [1] and F. Hausdorff [2]. Let $ \phi _ … WebThis paper studies Banach space valued Hausdorff-Young inequalities. The largest part considers ways of changing the underlying group. In particular the possibility to deduce the inequality for open subgroups as well as for quotient groups arising from compact subgroups is secured. A large body of results concerns the classical groupsT n ,R n … chassis moderne

Sharp inequalities for geometric Fourier transform and …

Category:Inequalities in Fourier Analysis on Rn PNAS

Tags:Hausdorff-young inequality

Hausdorff-young inequality

A Sharpened Hausdor -Young Inequality - University …

WebReverse Hausdorff Young for nonnegative functions. Asked 8 years, 4 months ago. Modified 8 years, 4 months ago. Viewed 1k times. 6. The classical Hausdorff-Young inequality states that. ‖ f ^ ‖ p ′ ≤ ‖ f ‖ p for 1 ≤ p ≤ 2. For p = 2, we even have equality due to Plancherel. If we additionally assume that f ≥ 0, we also get.

Hausdorff-young inequality

Did you know?

WebAbstract. This note describes two results: ( i) a sharp Hausdorff-Young inequality for the Fourier transform on Lp ( Rn) which extends an earlier result of Babenko; and ( ii) a sharp form of Young's inequality for the convolution of functions on Rn. That is, best possible constants are obtained for the following Lp ( Rn) inequalities: [Formula ... It has been shown in the first section that the Fourier transform maps L (R ) boundedly into L (R ) and L (R ) into itself. A similar argument shows that the Fourier series operator, which transforms periodic functions  f  : T → C into functions whose values are the Fourier coefficients The Hausdorff–Young inequality can also be established for the Fourier transform on locally compact Abelian groups. The norm estimate of 1 is not optimal. See the main article for references.

WebNov 21, 2003 · This result applies to yield a Hausdorff-Young inequality for nonunimodular groups. In this paper we deal with a definition of L p-Fourier transform on locally compact … WebJun 18, 2015 · Hausdorff-Young inequality on torus. 1. Inverse Hausdorff Young. 0. Understanding the proof of the Hausdorff-Young theorem. 1. Does the Hausdorff-Young inequality hold on bounded sets? 1. Hausdorff–Young inequality. 2. Interpolation inequality of fourier transformation. Hot Network Questions

WebMay 11, 2024 · In the proof of the proposition prior to this one (where B = R n ), we showed that the inequality ‖ f ^ ‖ L q ( R n) ≤ C ‖ f ‖ L p ( R n) gives us λ n λ − n / q ≤ C ~ λ n / p … WebMar 16, 2024 · The nonlinear Hausdorff-Young inequality follows from the work of Christ and Kiselev. Later Muscalu, Tao, and Thiele asked if the constants can be chosen independently of the exponent. We show that the nonlinear Hausdorff-Young quotient admits an even better upper bound than the linear one, provided that the function is …

WebMay 30, 2024 · In this paper, we prove several important sharp inequalities, including the Hausdorff-Young inequality and its converse, Pitt's inequality and Lieb's inequality for Clifford ambiguity functions.

WebOct 1, 2024 · The Hausdorff–Young inequality on Lie groups 103 this is a rephrasing of Hölder’s inequality for Hilsum’ s noncommutative L p spaces, T 1 ··· T k L r custom business forms minneapolisThe Hausdorff−Young inequality is a foundational result in the mathematical field of Fourier analysis. As a statement about Fourier series, it was discovered by William Henry Young (1913) and extended by Hausdorff (1923). It is now typically understood as a rather direct corollary of the Plancherel theorem, found in … See more Given a nonzero real number p, define the real number p' (the "conjugate exponent" of p) by the equation $${\displaystyle {\frac {1}{p}}+{\frac {1}{p'}}=1.}$$ If p is equal to one, … See more Equality is achieved in the Hausdorff-Young inequality for (multidimensional) Fourier series by taking See more Fourier series Given a function $${\displaystyle f:(0,1)\to \mathbb {C} ,}$$ one defines its "Fourier coefficients" as a … See more Here we use the language of normed vector spaces and bounded linear maps, as is convenient for application of the Riesz-Thorin … See more The condition p∈[1,2] is essential. If p>2, then the fact that a function belongs to $${\displaystyle L^{p}}$$, does not give any additional … See more chassis minageWebJun 30, 1998 · José L. Torrea. Contents §1. Introduction §2. General definitions and auxiliary results §3. Interpolation spaces §4. Interpolation and the Fourier type of Banach spaces §5. The Rademacher ... custom business forms printing