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, cilt.49, ss.1008-1022, 2008 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 49 Konu: 6
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1007/s11202-008-0097-6
  • Dergi Adı: SIBERIAN MATHEMATICAL JOURNAL
  • Sayfa Sayısı: ss.1008-1022

Özet

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.