Geodesic
Riesz transforms and partial derivatives
Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 445-451 
V. A. Yudin. Riesz transforms and partial derivatives. Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 445-451. http://geodesic.mathdoc.fr/item/SM_1991_69_2_a7/
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     author = {V. A. Yudin},
     title = {Riesz transforms and partial derivatives},
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     volume = {69},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_69_2_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

New estimates are given in the two-dimensional case for special operators that are linear combinations of Riesz transforms. They are used to investigate the distances between partial derivatives $\dfrac{\partial^nf}{\partial x_1^k\partial z_2^l}$, $k+l=n$, on the class $$ K_n=\biggl\{f\colon\biggl\|\frac{\partial^nf}{\partial{x_1^n}}\biggr\|_p\leqslant 1,\ \biggl\|\frac{\partial^nf}{\partial{x_1^n}}\biggr\|_p\leqslant 1\biggr\}, \qquad 1<p<\infty. $$

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