Necessary conditions for vector-valued operator inequalities in harmonic analysis

• Autores: Michael Christ, Andreas Seeger
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 93, Nº 2, 2006, págs. 447-473
• Idioma: inglés
• DOI: 10.1112/s0024611506015796
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• Resumen

  • 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.