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NECESSARY CONDITIONS FOR VECTOR-VALUED OPERATOR INEQUALITIES IN HARMONIC ANALYSIS

Published online by Cambridge University Press:  07 August 2006

MICHAEL CHRIST  and
ANDREAS SEEGER
MICHAEL CHRIST
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720-3840, USAmchrist@math.berkeley.edu
ANDREAS SEEGER
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USAseeger@math.wisc.edu
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Abstract

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.

Keywords

42B2542B1542B35
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 93 , Issue 2 , September 2006 , pp. 447 - 473
Copyright
2006 London Mathematical Society

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