Necessary conditions for vector-valued operator inequalities in harmonic analysis

Details Necessary conditions for vector-valued operator inequalities in harmonic analysis Necessary conditions for vector-valued operator inequalities in harmonic analysis

2005-04-01

arxiv.org/abs/math/0504030v1

Proceedings of the London Mathematical Society, 93, 2 (2006), 447-473.

Mathematics

Classical Analysis and ODEs

Scientific paper

Via a random construction we establish necessary conditions for $L^p(\ell^q)$ 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.

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