Abstract
A known Hardy-Littlewood theorem asserts that if both the function and its conjugate
are of bounded variation, then their Fourier series are absolutely convergent. It is proved in
the present paper that the same result holds true for functions on the whole axis and their
Fourier transforms, with certain adjustments. The proof of the original Hardy-Littlewood
theorem is derived from the obtained assertion. It turned out that the former is a partial
case of the latter when the function is supposed to be of compact support. A similar result
for radial functions is derived from the one-dimensional case.
Original language | American English |
---|---|
Pages (from-to) | 481-489 |
Number of pages | 9 |
Journal | Bulletin of the Institute of Mathematics Academia Sinica |
Volume | 8 |
Issue number | 4 |
State | Published - 2013 |