Necessary conditions for vector-valued operator inequalities in harmonic analysis
Christ, Michael · Seeger, Andreas
Original · EN
Via a random construction we establish necessary conditions for Lᵖ(ℓq) 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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