6 papers
Maximal directional singular integrals
Francesco Di Plinio, Ioannis Parissis
We survey maximal directional averages and directional singular integrals, and their connections with Kakeya--Nikodym phenomena, differentiation theory and the Carleson operator. T…
Endpoint estimates for multiparameter multipliers of Marcinkiewicz type
Odysseas Bakas, Ioannis Parissis
In this paper we prove sharp endpoint estimates for multiparameter Marcinkiewicz multiplier operators. More precisely, this result is a consequence of a more general theorem for mu…
The initial-to-final-state inverse problem with critically-singular potentials
Manuel Cañizares, Pedro Caro, Ioannis Parissis +1
The Schrödinger equation in high dimensions describes the evolution of a quantum system. Assume that we are given the evolution map sending each initial state $f\in L^2(\mathbb{R}^…
The initial-to-final-state inverse problem with time-independent potentials
Manuel Cañizares, Pedro Caro, Ioannis Parissis +1
The initial-to-final-state inverse problem consists in determining a quantum Hamiltonian assuming the knowledge of the state of the system at some fixed time, for every initial sta…
Singular multipliers on multiscale Zygmund sets
Odysseas Bakas, Valentina Ciccone, Francesco Di Plinio +3
Given an Orlicz space on , with submultiplicative Young function , we fully characterize the closed null sets of the rea…
Endpoint estimates for higher order Marcinkiewicz multipliers
Odysseas Bakas, Valentina Ciccone, Ioannis Parissis +1
We consider Marcinkiewicz multipliers of any lacunary order defined by means of uniformly bounded variation on each lacunary Littlewood--Paley interval of some fixed order $τ\geq 1…