Communications in Mathematical Analysis

Parabolic Singular Integrals on Ahlfors Regular Sets

J. Rivera-Noriega

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We present a survey of recent developments on a parabolic version of uniform rectifiability and parabolic singular integrals. In particular we describe some ideas to prove the equivalence between the parabolic uniform rectifiability of a set $E$ and the $L^2(E)$ boundedness of a class of Calder´on Zygmund integrals of parabolic type. We also describe a result on compactness of certain parabolic singular integrals, as well as some related open problems and conjectures.

Article information

Commun. Math. Anal., Volume 17, Number 2 (2014), 311-337.

First available in Project Euclid: 18 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory 35K08: Heat kernel

Parabolic uniform rectifiability parabolic singular integrals big pieces of parabolic Lipschitz graphs parabolic Corona type decompositions compact parabolic singular integrals


Rivera-Noriega, J. Parabolic Singular Integrals on Ahlfors Regular Sets. Commun. Math. Anal. 17 (2014), no. 2, 311--337.

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