The study of Hilbert transforms and oscillatory integrals has long been a focal point in harmonic analysis, embedding profound implications across pure and applied mathematics. The Hilbert transform, ...

Harmonic analysis occupies a central position in modern mathematical analysis by providing the tools to express complex functions as superpositions of simpler sinusoidal components via the Fourier ...

In the last twenty years there have been many connections discovered between fractal geometry and harmonic analysis. One such connection is a Fourier transform formula for the energy integral of a ...