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JesterTheAlias
JesterTheAlias
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As Bill Johnson has observed, rather more diplomatically than some people might haveThe answer is "not really, except in the answersense that currentlyCarlo Beenaker has been given (at time of writing) is grievously mistakenmentioned". 

I would advise both the original questioner, and the author of the answer, tosuggest you look at the discussion of the Hausdorff–Young inequality in Chapter IV Section 2 of Katznelson's Introduction to Harmonic Analysis (2nd edition, Dover). Probably there will also be the same cautionary remarks and salutary counterexamples in Edwards's book Fourier Series.

(Could someone please do me the favour of flagging this as CW?)

As Bill Johnson has observed, rather more diplomatically than some people might have, the answer that currently has been given (at time of writing) is grievously mistaken. I would advise both the original questioner, and the author of the answer, to look at the discussion of the Hausdorff–Young inequality in Chapter IV Section 2 of Katznelson's Introduction to Harmonic Analysis (2nd edition, Dover). Probably there will also be the same cautionary remarks and salutary counterexamples in Edwards's book Fourier Series.

(Could someone please do me the favour of flagging this as CW?)

The answer is "not really, except in the sense that Carlo Beenaker has mentioned". 

I suggest you look at the discussion of the Hausdorff–Young inequality in Chapter IV Section 2 of Katznelson's Introduction to Harmonic Analysis (2nd edition, Dover). Probably there will also be the same cautionary remarks and salutary counterexamples in Edwards's book Fourier Series.

(Could someone please do me the favour of flagging this as CW?)

Source Link
JesterTheAlias
JesterTheAlias
  • 26
  • 1
  • 3

As Bill Johnson has observed, rather more diplomatically than some people might have, the answer that currently has been given (at time of writing) is grievously mistaken. I would advise both the original questioner, and the author of the answer, to look at the discussion of the Hausdorff–Young inequality in Chapter IV Section 2 of Katznelson's Introduction to Harmonic Analysis (2nd edition, Dover). Probably there will also be the same cautionary remarks and salutary counterexamples in Edwards's book Fourier Series.

(Could someone please do me the favour of flagging this as CW?)