Pointwise and integral estimates for the B-Riesz potential in terms of B-maximal and B-fractional maximal functions


Guliev V. S. , GARAKHANOVA N., ZEREN Y.

SIBERIAN MATHEMATICAL JOURNAL, vol.49, no.6, pp.1008-1022, 2008 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 6
  • Publication Date: 2008
  • Doi Number: 10.1007/s11202-008-0097-6
  • Journal Name: SIBERIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1008-1022

Abstract

We study the maximal and fractional maximal functions and Riesz potentials that are generated by the generalized shift operator associated with the Laplace-Bessel operator. We obtain some pointwise and integral estimates that give a relation between the B-maximal and B-fractional maximal functions and B-Riesz potentials and extend the available results to the objects of a more general nature. Basing on these results, we prove interpolation theorems for the B-fractional maximal functions and B-Riesz potentials.