An Embedding Theorem for Functions whose Fourier Transforms are Weighted Square Summable | Zendy

Victor Katsnelson | Zendy

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An Embedding Theorem for Functions whose Fourier Transforms are Weighted Square Summable

Author(s) -

Victor Katsnelson

Publication year - 1994

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/506

Subject(s) - embedding , mathematics , fourier transform , square (algebra) , parseval's theorem , fourier inversion theorem , fourier analysis , pure mathematics , mathematical analysis , computer science , fractional fourier transform , geometry , artificial intelligence

Our main result is, by elementary means only, an embedding theorem for functions f whose Fourier transforms I are weight square summable, i.e. f,, 1f( A )1 2w ( A ) d\ < oo, where the weight function w : 1k" (0,00) satisfies the Kolmogorov condition fe,, w.)'dA < co. The necessary and sufficient condition on a non-negative Borelian measure on 1k" is given, for the inequality f,. f(t)I 2 (dt) < A f If(A )1 2w ( A )d,\ to be hold for every such function 1, with a constant A < oo not depending on f.

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