Geodesic
Weak type (1,1) in a Refinement of the Marcinkiewicz Theorem
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 3, pp. 89-92

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Let $m$ be a bounded function on $\mathbb{R}_+$ whose $p$-variations on the intervals $[2^k,2^{k+1}]$, $k\in\mathbb{Z}$, are uniformly bounded for some $p2$. Then the operator $T$, $\widehat{Tf}=m\hat f$, is of weak type $(1,1)$ on the space $H^1(\mathbb{R})$.
Mots-clés : Fourier multiplier. 
@article{FAA_2009_43_3_a6,
     author = {S. V. Kislyakov},
     title = {Weak type (1,1) in a {Refinement} of the {Marcinkiewicz} {Theorem}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {89--92},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2009_43_3_a6/}
}
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S. V. Kislyakov. Weak type (1,1) in a Refinement of the Marcinkiewicz Theorem. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 3, pp. 89-92. http://geodesic.mathdoc.fr/item/FAA_2009_43_3_a6/