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
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