Tobias Mattsson: Sparse Domination and Regularity Properties of Oscillatory and Fourier Integral Operators in Harmonic Analysis

Abstract

 We show regularity results for a broad class of oscillatory and Fourier integral operators, acting on Besov-Lipschitz and Triebel-Lizorkin spaces. These results lead to improved regularity estimates for solutions to classes of partial differential equations. In addition, we also show new sparse domination results for these operators in paper III, providing weighted, and vector-valued inequalities, and weak (1,1) estimates as consequences. This later framework not only strengthens known bounds but also gives precise quantitative control of operator norms.