JGeomAnal https://doi.org/10.1007/s12220-018-0038-y A Constrained Optimization Problem for the Fourier Transform: Quantitative Analysis Dominique Maldague Received: 15 March 2018 © Mathematica Josephina, Inc. 2018 Abstract Among functions f majorized by indicator functions 1 , which functions 1/p have maximal ratio f /|E | ? We establish a quantitative answer to this question for exponents q sufﬁciently close to even integers, building on previous work proving the existence of such maximizers. Keywords Harmonic analysis · Extremization · Fourier transform · Quantitative analysis Mathematics Subject Classiﬁcation 42A16 · 42B10 1 Introduction −2πix ·ξ Deﬁne the Fourier transform as F ( f )(ξ ) = f (ξ ) = e f (x )dx for a d 1 d function f : R → C. The Fourier transform is a contraction from L (R ) to ∞ d 2 d L (R ) and is unitary on L (R ). Interpolation gives the Hausdorff–Young inequal- 1 1 ity f f , where p ∈ (1, 2),1 = + .In, Beckner proved the sharp q p p q Hausdorff–Young inequality f C f , (1.1) q p 1/2 p −1/2q where C = p
The Journal of Geometric Analysis – Springer Journals
Published: May 29, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera