Inequalities in Fourier Analysis on  R n  | Zendy

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Inequalities in Fourier Analysis on R ⁿ

Author(s) -

William Beckner

Publication year - 1975

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.011

H-Index - 771

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.72.2.638

Subject(s) - convolution (computer science) , inequality , mathematics , fourier transform , fourier analysis , hausdorff space , young's inequality , combinatorics , pure mathematics , mathematical analysis , linear inequality , rearrangement inequality , computer science , machine learning , artificial neural network

This note describes two results: (i ) a sharp Hausdorff-Young inequality for the Fourier transform onLp (Rn ) which extends an earlier result of Babenko; and (ii ) a sharp form of Young's inequality for the convolution of functions onRn . That is, best possible constants are obtained for the followingLp (Rn ) inequalities: [Formula: see text]

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