Paolo Ciatti & Alessio Martini 
Geometric Aspects of Harmonic Analysis 

This volume originated in talks given in Cortona at the conference ‘Geometric aspects of harmonic analysis’ held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables.




The work is addressed to researchers in the field.

Table of Content

– An Extension Problem and Hardy Type Inequalities for the Grushin Operator. – Sharp Local Smoothing Estimates for Fourier Integral Operators. – On the Hardy–Littlewood Maximal Functions in High Dimensions: Continuous and Discrete Perspective. – Potential Spaces on Lie Groups. – On Fourier Restriction for Finite-Type Perturbations of the Hyperbolic Paraboloid. – On Young’s Convolution Inequality for Heisenberg Groups. – Young’s Inequality Sharpened. – Strongly Singular Integrals on Stratified Groups. – Singular Brascamp–Lieb: A Survey. – On the Restriction of Laplace–Beltrami Eigenfunctions and Cantor-Type Sets. – Basis Properties of the Haar System in Limiting Besov Spaces. – Obstacle Problems Generated by the Estimates of Square Function. – Of Commutators and Jacobians. – On Regularity and Irregularity of Certain Holomorphic Singular Integral Operators.