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A rearrangement estimate for the generalized multilinear fractional integrals

Abstract

We study the \(L_{p_1 } \times L_{p_2 } \times \cdots \times L_{p_k } \) boundedness of generalized multilinear fractional integrals. An O’Neil type inequality for a k-linear integral operator is proved. Using an O’Neil type inequality for a k-linear integral operator, we obtain a pointwise rearrangement estimate of generalized multilinear fractional integrals. By way of application we prove a Sobolev type theorem for these integrals.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 3, pp. 577–585, May–June, 2007.

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Guliyev, V.S., Nazirova, S.A. A rearrangement estimate for the generalized multilinear fractional integrals. Sib Math J 48, 463–470 (2007). https://doi.org/10.1007/s11202-007-0048-7

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Keywords

  • Lebesgue space
  • O’Neil type inequality
  • rearrangement estimate
  • generalized multilinear fractional integral