A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains
Studia Mathematica, Tome 140 (2000) no. 3, pp. 273-287
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
It is proved that if $m : ℝ^d → ℂ$ satisfies a suitable integral condition of Marcinkiewicz type then m is a Fourier multiplier on the $H^1$ space on the product domain $ℝ^{d_1}×...×ℝ^{d_k}$. This implies an estimate of the norm $N(m,L^p(ℝ^d)$ of the multiplier transformation of m on $L^p(ℝ^d)$ as p→1. Precisely we get $N(m,L^p(ℝ^d))≲(p-1)^{-k}$. This bound is the best possible in general.
@article{10_4064_sm_140_3_273_287,
author = {Micha{\l} Wojciechowski},
title = {A {Marcinkiewicz} type multiplier theorem for {H{\textonesuperior}} spaces on product domains},
journal = {Studia Mathematica},
pages = {273--287},
publisher = {mathdoc},
volume = {140},
number = {3},
year = {2000},
doi = {10.4064/sm-140-3-273-287},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-140-3-273-287/}
}
TY - JOUR AU - Michał Wojciechowski TI - A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains JO - Studia Mathematica PY - 2000 SP - 273 EP - 287 VL - 140 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-140-3-273-287/ DO - 10.4064/sm-140-3-273-287 LA - fr ID - 10_4064_sm_140_3_273_287 ER -
%0 Journal Article %A Michał Wojciechowski %T A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains %J Studia Mathematica %D 2000 %P 273-287 %V 140 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-140-3-273-287/ %R 10.4064/sm-140-3-273-287 %G fr %F 10_4064_sm_140_3_273_287
Michał Wojciechowski. A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains. Studia Mathematica, Tome 140 (2000) no. 3, pp. 273-287. doi: 10.4064/sm-140-3-273-287
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