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On Multilinear Fractional Integrals Generated by the Quasi-distance

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Author(s): Hüseyin Yıldırım | Mehmet Zeki Sarıkaya | Umut Mutlu Ozkan

Journal: Selçuk Journal of Applied Mathematics
ISSN 1302-7980

Volume: 8;
Issue: 2;
Start page: 101;
Date: 2007;
Original page

Keywords: Fractional Integral | Riesz Potential | Quasi-distance.

ABSTRACT
In Rⁿ, we prove L^{p₁}×...×L^{p_{k}} boundedness for the multilinear fractional integrals generated by the quasi-distanceI_{α,λ,v}(f₁,...,f_{k})(x)=∫f₁(x-θ₁y)f₂(x-θ₂y)...f_{k}(x-θ_{k}y)‖y‖_{λ,v}^{α-n}dywhere the θ_{j}'s are nonzero and distinct. We also prove multilinear versions of two inequalities for fractional integrals and a multilinear Lebesgue differentiation theorem.
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