Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-12-01T03:04:24.899Z Has data issue: false hasContentIssue false
  • English
  • Français

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, [email protected]
ANDREAS SEEGER
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)