ON THE BOUUNDEDNESS OF FRACTIONAL B-MAXIMAL OPERATORS IN THE LORENTZ SPACES Lp,q,gamma >(R(+)n)

AYKOL KOCAKUŞAKLI C., ŞERBETÇİ A.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, vol.17, no.2, pp.27-38, 2009 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2009
  • Journal Name: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.27-38
  • Keywords: Laplace-Bessel differential operator, generalized shift operator, gamma-rearrangement, Lorentz spaces, B-maximal function, fractional B-maximal function, BESSEL DIFFERENTIAL OPERATOR, BOUNDEDNESS, INEQUALITY
  • Ankara University Affiliated: Yes

Abstract

In this study, sharp rearrangement inequalities for the fractional B-maximal function M(alpha,gamma)f are obtained in the Lorentz spaces L-p,L-q,L-gamma and by using these inequalities the boundedness conditions of the operator M-alpha,M-gamma are found. Then, the conditions for the boundedness of the B-maximal operator M-gamma are obtained in L-p,L-q,L-gamma.