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Original Articles

Weighted estimates of truncated potential kernels in the variable exponent setting

Pages 813-828 | Received 04 Nov 2009, Accepted 15 Feb 2010, Published online: 06 Oct 2010
 

Abstract

In connection with the applications to the study of classical operators of harmonic analysis in variable exponents Morrey spaces, we prove estimates of weighted norms of potential kernels truncated to balls B(x, r). We admit a class of radial type weights. The conditions on the validity of estimates are given in terms of Zygmund type inequalities on weight or in terms of their Matuszewska–Orlich indices

AMS Subject Classifications::

Acknowledgements

This work was supported by Russian Federal Targeted Programme ‘Scientific and Research-Educational Personnel of Innovative Russia’ for 2009–2013, project No. 02.740.11.5024.

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