  Lim et al. (2023) have recently proposed that the slope ($\delta$) of the
power law distribution between the energy flux and oscillation frequency could
determine whether high-frequency transverse oscillations give a dominant
contribution to the heating ($\delta<1$). A meta-analysis of decayless
transverse oscillations revealed that high-frequency oscillations potentially
play a key role in heating the solar corona. We aim to investigate how
(whether) the distributions of the energy flux contained in transverse
oscillations, and their slopes, depend on the coronal region in which the
oscillation occurs. We analyse transverse oscillations from 41 quiet Sun (QS)
loops and 22 active region (AR) loops observed by Solar Orbiter/Extreme
Ultraviolet Imager (SolO/EUI) HRIEUV. The energy flux and energy are estimated
using analysed oscillation parameters and loop properties, such as periods,
displacement amplitudes, loop lengths, and minor radii of the loops. It is
found that about 71% of QS loops and 86% of AR loops show decayless
oscillations. We find that the amplitude does not change depending on different
regions, but the difference in the period is more pronounced. Although the
power law slope ($\delta=-1.79$) in AR is steeper than that ($\delta=-1.59$) in
QS, both of them are significantly less than the critical slope of 1. Our
statistical study demonstrates that high-frequency transverse oscillations can
heat the QS. For ARs, the total energy flux is insufficient unless
yet-unobserved oscillations with frequencies up to 0.17 Hz are present. Future
EUI campaigns will be planned to confirm this.
