We prove that some inequalities, which are considered to be generalizations of Hardy's inequality on the circle, can be modified and proved to be true for functions integrable on the real line. In fact we would like to show that some constructions that were used to prove the Littlewood conjecture can be used similarly to produce real Hardy-type inequalities. This discussion will lead to many questions concerning the relationship between Hardy-type inequalities on the circle and those on the real line.

Keywords:

Hardy's inequality, inequalities including the Fourier transform and Hardy spaces Hardy's inequality, inequalities including the Fourier transform and Hardy spaces

MSC Classifications:

42A05, 42A99 show english descriptions Trigonometric polynomials, inequalities, extremal problems
None of the above, but in this section 42A05 - Trigonometric polynomials, inequalities, extremal problems
42A99 - None of the above, but in this section

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