Fourier Decay Under a Radial Ibaguner Fractal Operator A Rigorous Component of the Falconer-IFO Program

Key Points

• This research aims to explore the Fourier decay properties of measures under a radial Ibaguner Fractal Operator.
• Analyzed Fourier decay of measures using a radial Ibaguner Fractal Operator.
• Established decay rates for Frostman measures of dimension s.
• Examined sharp dimensional thresholds for positivity of IFO-distance sets.
• Demonstrated a specific decay rate for pushforward measures under Hlder-type contraction.
• Identified a clear dimensional threshold for the associated IFO-distance set.