On boundedness of the generalized B-potential integral operators in the Lorentz spaces

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

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, cilt.18, sa.12, ss.885-895, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 12
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1080/10652460701510980
  • Dergi Adı: INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.885-895
  • Anahtar Kelimeler: Laplace-Bessel differential operator, O'Neil type inequality, generalized B-potential integrals, B-fractional integral, Lorentz spaces
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we study the convolution operator (B-convolution), and the generalized B-potential integral and fractional integral (B-fractional integral) with rough kernel, associated with the Laplace-Bessel differential operator Delta(B) = Sigma(k)(i=1) B-i + Sigma(n)(j=k+1)(partial derivative(2)/partial derivative x(j)(2)), B-i = (partial derivative(2)/partial derivative x(i)(2)) + (gamma(i)/x(i))(partial derivative/partial derivative x(i)). We get O'Neil type inequality for the B-convolution. By using O'Neil type inequality we obtain a pointwise rearrangement estimate of the generalized B-potential integral. We prove the boundedness of the generalized B-potential integral operator in the Lorentz spaces, and the proof is based on the pointwise estimate of the rearrangement of this operator.