A theorem on weak type estimates for Riesz transforms and martingale transforms
Annales de l'Institut Fourier, Volume 31 (1981) no. 1, pp. 257-264.

The Riesz transforms of a positive singular measure νM(R n ) satisfy the weak type inequality

mj=1n|Rjν|>λCνλ,λ>0

where m denotes Lebesgue measure and C is a positive constant only depending on m.

Les transformées de Riesz d’une mesure positive singulière νM(R n ) satisfont à l’inégalité faible

mj=1n|Rjν|>λCνλ,λ>0

m est la mesure de Lebesgue et C une constante positive dépendant de n.

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     author = {Varopoulos, Nicolas Th.},
     title = {A theorem on weak type estimates for {Riesz} transforms and martingale transforms},
     journal = {Annales de l'Institut Fourier},
     pages = {257--264},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {31},
     number = {1},
     year = {1981},
     doi = {10.5802/aif.826},
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Varopoulos, Nicolas Th. A theorem on weak type estimates for Riesz transforms and martingale transforms. Annales de l'Institut Fourier, Volume 31 (1981) no. 1, pp. 257-264. doi : 10.5802/aif.826. https://aif.centre-mersenne.org/articles/10.5802/aif.826/

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