Rough maximal bilinear singular integrals

  • Eva Buriánková
  • Petr HonzíkEmail author


We study the rough maximal bilinear singular integral
$$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/|(y,z)|)}{ |(y,z)|^{2n}}f(x-y)g(x-z) dydz\right| , \end{aligned}$$
where \(\varOmega \) is a function in \(L^\infty (\mathbb S^{2n-1})\) with vanishing integral. We prove it is bounded from \(L^p\times L^q\rightarrow L^r,\) where \(1<p,q<\infty \) and \(1/r=1/p+1/q.\) We also discuss results for \(\varOmega \in L^s(\mathbb S^{2n-1}),\)\(1<s<\infty \).


Singular integrals Bilinear operators Maximal operators Fourier multipliers 

Mathematics Subject Classification

42B20 42B99 



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Copyright information

© Universitat de Barcelona 2019

Authors and Affiliations

  1. 1.Charles UniversityPrague 8Czech Republic

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