Inequality of O'Neil-type for convolutions associated with the Laplace-Bessel differential operator and applications

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

MATHEMATICAL INEQUALITIES & APPLICATIONS, cilt.11, sa.1, ss.99-112, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 1
  • Basım Tarihi: 2008
  • Doi Numarası: 10.7153/mia-11-06
  • Dergi Adı: MATHEMATICAL INEQUALITIES & APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.99-112
  • Anahtar Kelimeler: Laplace-Bessel differential operator, B-convolution, rearrangement of a function, O'Neil type inequality, B-fractional integral, Fractional B-maximal function
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper we prove an O'Neil-type inequality for the convolution operator ( B-convolution) associated with the Laplace-Bessel differential operator. By using an O'Neil-type inequality for rearrangements we obtain a pointwise rearrangement estimate of the B-convolution. As an application, we obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional B-maximal operator and B-fractional integral operator with rough kernels from the spaces L-p,L-gamma to L-q,L-gamma and from the spaces L-1,(gamma) to the weak spaces WLq,gamma.