Weighted estimates of truncated potential kernels in the variable exponent setting

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

Keywords:

• variable exponent space
• Morrey space
• potential kernel
• radial weights
• Matuszewska–Orlica indices

AMS Subject Classifications::

• 46E30
• 42B35

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.