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

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

m∑j=1n|Rjν|>λ≥C∥ν∥λ,λ>0

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

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

m∑j=1n|Rjν|>λ≥C∥ν∥λ,λ>0

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

@article{AIF_1981__31_1_257_0,
     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},
     zbl = {0437.60003},
     mrnumber = {84e:60070},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.826/}
}
TY  - JOUR
AU  - Varopoulos, Nicolas Th.
TI  - A theorem on weak type estimates for Riesz transforms and martingale transforms
JO  - Annales de l'Institut Fourier
PY  - 1981
SP  - 257
EP  - 264
VL  - 31
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.826/
DO  - 10.5802/aif.826
LA  - en
ID  - AIF_1981__31_1_257_0
ER  - 
%0 Journal Article
%A Varopoulos, Nicolas Th.
%T A theorem on weak type estimates for Riesz transforms and martingale transforms
%J Annales de l'Institut Fourier
%D 1981
%P 257-264
%V 31
%N 1
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.826/
%R 10.5802/aif.826
%G en
%F AIF_1981__31_1_257_0
Varopoulos, Nicolas Th. A theorem on weak type estimates for Riesz transforms and martingale transforms. Annales de l'Institut Fourier, Tome 31 (1981) no. 1, pp. 257-264. doi : 10.5802/aif.826. https://aif.centre-mersenne.org/articles/10.5802/aif.826/

[1] E.M. Stein, Singular integrals and differentiability properties of functions, Princeton University press (1970). | MR | Zbl

[2] Cereteli, Mat. Zametki, t. 22 No. 5 (1977).

[3] R.F. Gundy, On a Theorem of F. and M. Riesz and an Identity of A. Wald. (preprint). | Zbl

[4] L. Loomis, A note on the Hilbert transform, B.A.M.S., 52 (1946), 1082-1086. | MR | Zbl

[5] K. Murali Rao, Quasi-Martingales, Math. Scand., 24 (1969), 79-92. | EuDML | MR | Zbl

[6] S. Janson, Characterizations of H1 by singular integral transforms on martingales and Rn, Math. Scand., 41 (1977), 140-152. | EuDML | MR | Zbl

Cité par Sources :