Necessary conditions for vector-valued operator inequalities in harmonic analysis
Classical Analysis and ODEs
2010-03-15 v1
Abstract
Via a random construction we establish necessary conditions for inequalities for certain families of operators arising in harmonic analysis. In particular we consider dilates of a convolution kernel with compactly supported Fourier transform, vector maximal functions acting on classes of entire functions of exponential type, and a characterization of Sobolev spaces by square functions and pointwise moduli of smoothness.
Cite
@article{arxiv.math/0504030,
title = {Necessary conditions for vector-valued operator inequalities in harmonic analysis},
author = {Michael Christ and Andreas Seeger},
journal= {arXiv preprint arXiv:math/0504030},
year = {2010}
}