On the rearrangement estimates and the boundedness of the generalized fractional integrals associated with the Laplace-Bessel differential operator

Guliyev V. S., Safarov Z. V., ŞERBETÇİ A.

ACTA MATHEMATICA HUNGARICA, cilt.119, sa.3, ss.201-217, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 119 Sayı: 3
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1007/s10474-007-6107-5
  • Dergi Adı: ACTA MATHEMATICA HUNGARICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.201-217
  • Anahtar Kelimeler: Laplace-Bessel differential operator generalized shift operator, B-convolution, O'Neil type inequality, generalized B-fractional integral
  • Ankara Üniversitesi Adresli: Evet

Özet

We introduce the generalized fractional integrals (generalized B-fractional integrals) generated by the Delta(B) Laplace-Bessel differential operator and give some results for them. We obtain O'Neil type inequalities for the B-convolutions and give pointwise rearrangement estimates of the generalized B-fractional integrals. Then we get the L (p,gamma) -boundedness of the generalized B-convolution operator, the generalized B-Riesz potential and the generalized fractional B-maximal function. Finally, we prove a sharp pointwise estimate of the nonincreasing rearrangement of the generalized fractional B-maximal function.