This article is cited in 4 papers

A rearrangement estimate for the generalized multilinear fractional integrals

V. S. Guliev^a, Sh. A. Nazirova<sup>b

a</sup> Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences
^b Khazar University

Abstract: We study the $L_{p_1}\times L_{p_2}\times\ldots\times L_{p_k}$ 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.

Keywords: Lebesgue space, O'Neil type inequality, rearrangement estimate, generalized multilinear fractional integral.

UDC: 517.51

Received: 17.10.2005

 English version: Siberian Mathematical Journal, 2007, 48:3, 463–470

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