Necessary and sufficient conditions for the boundedness of rough B-fractional integral operators in the Lorentz spaces

Guliyev V. S., ŞERBETÇİ A., Ekincioglu I.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.336, no.1, pp.425-437, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 336 Issue: 1
  • Publication Date: 2007
  • Doi Number: 10.1016/j.jmaa.2007.02.080
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.425-437
  • Keywords: Laplace-Bessel differential operator, B-convolution O'Neil type inequality, fractional B-maximal function, B-fractional integral, Lorentz space
  • Ankara University Affiliated: Yes

Abstract

In this paper, the necessary and sufficient conditions are found for the boundedness of the rough B-fractional interal operators from the Lorentz spaces L (P.s.gamma) to L (q ,r ,gamma) , 1 < p < q < infinity, 1 <= r <= s <= infinity, and from L-1 .r . gamma to L-q,L- infinity,L-gamma W L-q,L-gamma, 1 < q < infinity, 1 <= r <= infinity. As a consequence of this, the same results are given for the fractional B-maximal operator and B-Riesz potential. (c) 2007 Elsevier Inc. All rights reserved.