Some remarks on multilinear maps and interpolation

By Loukas Grafakos, Nigel J. Kalton. 2001

151 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a7355a344ff382de3f2533325e8e5dbe16a1d43d

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In Applied Mathematics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

The Multilinear Strong Maximal Function (2010, background): “The result is not bilinear per se, as the first function remains in the same space during the interpolation, however, it only requires two initial conditions instead of three required in the classical real-method bilinear interpolation, see for instance [10].”
On multilinear singular integrals of Calderón-Zygmund type (2002, methodology): “See the articles of Grafakos and Kalton [32], Janson [41], and also Strichartz [55] for a reference on multilinear interpolation.”
Multilinear analysis on metric spaces (2014, background): “Applications include the boundedness of paraproducts and bilinear multiplier operators on products of Besov and Triebel–Lizorkin spaces.”
Weighted inequalities for multilinear fractional integral operators (2009, background): “Multilinear fractional integral operators were studied by Grafakos [7], Kenig and Stein [12], Grafakos and Kalton [ 9 ].”
Compactness properties of commutators of bilinear fractional integrals (2013, background): “These operators were first introduced by Grafakos in [11], and l ter studied by Grafakos and Kalton [12] and Kenig and Stein [16].”
Extrapolation of Weighted norm inequalities for multivariable operators and applications (2004, methodology): “Applying the multilinear Marcinkiewicz interpolation theorem (see for instance [8] Theorem 4.”
Multilinear generalized Radon transforms and point configurations (2012, background): “(See [12, 27, 13] for more singular operators of fractional integral type.”
The Hörmander multiplier theorem for multilinear operators (2012, background): “Multilinear interpolation ([7], [1]) yields that Tσ is bounded from Lp1(Rn)× · · · × Lpm(Rn) to Lp(Rn) for all indices pj satisfying 1 < p1, .”