On weighted Fourier inequalities - some new scales of equivalent conditions

0544041 - MÚ 2022 RIV HR eng J - Journal Article
Kufner, Alois - Persson, L. E. - Samko, N.
On weighted Fourier inequalities - some new scales of equivalent conditions.
Journal of Mathematical Inequalities. Roč. 15, č. 2 (2021), s. 879-898. ISSN 1846-579X. E-ISSN 1846-579X
Institutional support: RVO:67985840
Keywords : continuity of the Fourier operator * Fourier inequalities * Fourier transform * Hardy-type inequalities
OECD category: Pure mathematics
Impact factor: 1.145, year: 2021
Method of publishing: Open access
https://dx.doi.org/10.7153/jmi-2021-15-61

For Lebesgue spaces on ℝn, we study two-weight p → q-inequalities for Fourier transform. Some sufficient conditions on weights for such inequalities are known for special ranges of parameters p and q. In the same ranges of parameters we show, that in every case each of those conditions can be replaced by infinitely many conditions, even by continuous scales of conditions. We also derive some new such characterizations concerning the Fourier transform in weighted Lorentz spaces.
Permanent Link: http://hdl.handle.net/11104/0321101