Canad. Math. Bull. 54(2011), 159-171
Printed: Mar 2011
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.
Hardy's inequality, inequalities including the Fourier transform and Hardy spaces
42A05 - Trigonometric polynomials, inequalities, extremal problems
42A99 - None of the above, but in this section