Hausdorff-young inequality
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 … WebJSTOR Home
Hausdorff-young inequality
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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, … 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 …
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 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 ...
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 … 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 WebJul 12, 2024 · The Hausdorff–Young inequality on Lie groups @article{Cowling2024TheHI, title={The Hausdorff–Young inequality on Lie groups}, author={Michael G. Cowling and Alessio Martini and Detlef M{\"u}ller and Javier Parcet}, journal={Mathematische Annalen}, year={2024}, pages={1-39} } M. Cowling
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 …
WebIn Q5, the good lambda inequality should require f^# to be less than eps lambda, rather than greater than eps lambda. ... Young’s inequality, Hausdorff-Young, Christ-Kiselev. (updated, Dec 6. Erratum, Dec 23 2024: In the definition of f (and its Fourier transform) on page 21, a factor of exp( -pi i n^2 v ^2) should be added.) tif znacenje<2$, and further … tif zu jpgWebReverse 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. tifton ga jacuzzi suitesWebTogether with the Plancherel identity and Hausdorff–Young inequality, we establish Lp(R2) multiplier theory and Littlewood–Paley theorems associated with the 2D-LCT. As applications, we demonstrate the recovery of the L1(R2) signal function by simulation. Moreover, we present a real-life application of such a theory of 2D-LCT by encrypting ... tif zu svgWebrem (QSP), the quantum Hausdorff–Young inequality (QHY) with 1=p +1=q =1, the quantum Young inequality (QY) with 1=p +1=q =1+1=r, and the basic quantum … batubara jambiWebMay 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. tig 141 poziomyhttp://helper.ipam.ucla.edu/publications/ccgws3/ccgws3_11829.pdf batubara kalimantan tengah