Harmonic and Functional Analysis - AHF

Reference of the Group:

GIUV2023-556

 
Description of research activity:

The aim of this research group is to advance in the study of different harmonic, functional and complex analysis problems. Regarding harmonic analysis, the topics of interest are mainly the study of problems related to the Fourier transform restriction phenomenon to null measurement sets. This includes, for example, space-time estimates for solutions to the wave equation and the Schrödinger equation or estimates for maximal functions associated with manifolds. Likewise, the analysis of both linear and bilinear Fourier multipliers acting on different function spaces and different groups is included. Problems related to the control of oscillatory operators by positive operators in the context of sparse domination or weighted inequalities will also be studied. In relation to functional and complex analysis problems, we aim to analyse the binding of defined operators on spaces of analytic functions both with scalar and vector values, such as the composition operator or the Cesaro operator, among others. Likewise, the study of approximation in function spaces through greedy bases is also included.

 
Web:

No Determinada

 
Scientific-technical goals:
  • Advance the study of "local smoothing" inequalities for the wave equation.
  • characterization of linear and bilinear multipliers in L^p and in other function spaces
  • Study "sparse" dominance on the "endpoint" for different operators
  • Study the delimitation of classical operators on Hardy and Bergman spaces
 
Research lines:
  • Harmonic Analysis.Study of problems related to the Fourier phenomena transform restriction to null sets, maximal functions and linear and bilinear Fourier multipliers.
  • Functional and Complex Analysis.Study of classical operators on analytical function spaces and approximation problems using greedy bases.
 
Group members:
Name Nature of participation Entity Description
OSCAR FCO BLASCO DE LA CRUZDirectorUniversitat de València
Research team
DAVID BELTRAN PORTALESMemberUniversitat de València
 
CNAE:
  • -
 
Associated structure:
  • Mathematical Analysis
 
Keywords:
  • MAXIMAL FUNCTIONS
  • FOURIER MULTIPLIERS
  • FOURIER RESTRICTION
  • BASES
  • HARDY SPACES
  • CESAR OPERATORS