The Hausdorff operators on the real Hardy spaces $H^p({\Bbb R})$
Studia Mathematica, Tome 148 (2001) no. 1, pp. 37-45
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We prove that the Hausdorff operator generated by a function
$\phi $ is bounded on the real Hardy space
$H^p({\mathbb R})$, $0 p \le 1,$ if the Fourier transform
$\widehat {\phi }$ of $\phi $ satisfies certain
smoothness conditions. As a special case, we obtain the
boundedness of the Ces\accent18 aro operator of order $\alpha $
on $H^p({\mathbb R})$, $2/(2\alpha +1) p \le 1$. Our proof is
based on the atomic decomposition and molecular characterization
of $H^p({\mathbb R})$.
Keywords:
prove hausdorff operator generated function phi bounded real hardy space mathbb fourier transform widehat phi phi satisfies certain smoothness conditions special obtain boundedness ces accent aro operator order alpha mathbb alpha proof based atomic decomposition molecular characterization mathbb
Affiliations des auteurs :
Yuichi Kanjin 1
@article{10_4064_sm148_1_4,
author = {Yuichi Kanjin},
title = {The {Hausdorff} operators on the real {Hardy} spaces $H^p({\Bbb R})$},
journal = {Studia Mathematica},
pages = {37--45},
year = {2001},
volume = {148},
number = {1},
doi = {10.4064/sm148-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm148-1-4/}
}
Yuichi Kanjin. The Hausdorff operators on the real Hardy spaces $H^p({\Bbb R})$. Studia Mathematica, Tome 148 (2001) no. 1, pp. 37-45. doi: 10.4064/sm148-1-4
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