%0 Journal Article %A Kakizawa, RyƓhei %T Equivalent conditions for the validity of the Helmholtz decomposition of Muckenhoupt $A_{p}$-weighted $L^{p}$-spaces %J Czechoslovak Mathematical Journal %D 2018 %P 771-789 %V 68 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0646-16/ %R 10.21136/CMJ.2018.0646-16 %G en %F 10_21136_CMJ_2018_0646_16