On multilinear fractional integrals

Loukas Grafakos

ArticleOriginal scientific text

Title

On multilinear fractional integrals

Authors ¹

Affiliations

Department of Mathematics, Yale University, Box 2155, Yale Station, New Haven, Connecticut 06520, U.S.A.

Abstract

In

ℝ^{n}

, we prove

L^{p ₁} \times ... \times L^{p_{K}}

boundedness for the multilinear fractional integrals

I_{α} (f ₁, ..., f_{K}) (x) = ʃ f ₁ (x - θ ₁ y) ... f_{K} (x - θ_{K} y) {| y |}^{α - n} d y

where 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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Title

On multilinear fractional integrals

Affiliations

Abstract

Bibliography