Let be an arbitrary Young function and be a compact set in having (O)-property. Then there exists a constant independent of such that
for all and , where , , is the Fourier transform of and is the Luxemburg norm. As an application, a new Paley–Wiener theorem is given.
"An improvement of Bernstein’s inequality for functions in Orlicz spaces with smooth Fourier image." Rocky Mountain J. Math. 52 (1) 29 - 42, February 2022. https://doi.org/10.1216/rmj.2022.52.29