The Riesz transforms of a positive singular measure satisfy the weak type inequality
where denotes Lebesgue measure and is a positive constant only depending on .
Les transformées de Riesz d’une mesure positive singulière satisfont à l’inégalité faible
où est la mesure de Lebesgue et une constante positive dépendant de .
@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, Volume 31 (1981) no. 1, pp. 257-264. doi : 10.5802/aif.826. https://aif.centre-mersenne.org/articles/10.5802/aif.826/
[1] Singular integrals and differentiability properties of functions, Princeton University press (1970). | MR | Zbl
,[2]
, Mat. Zametki, t. 22 No. 5 (1977).[3] On a Theorem of F. and M. Riesz and an Identity of A. Wald. (preprint). | Zbl
,[4] A note on the Hilbert transform, B.A.M.S., 52 (1946), 1082-1086. | MR | Zbl
,[5] Quasi-Martingales, Math. Scand., 24 (1969), 79-92. | EuDML | MR | Zbl
,[6] Characterizations of H1 by singular integral transforms on martingales and Rn, Math. Scand., 41 (1977), 140-152. | EuDML | MR | Zbl
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