$$ u:\overline {B_1(0)}\subset\mathbb{R^2}\to\mathbb{R} $$ defined by : $$ u(x_1,x_2)=x_1x_2(1-\sqrt{x_1^2+x_2^2}) $$ Can I at first consider $$ x_1x_2 $$ and look if $$ x_1x_2\in C^{l,\alpha}(\overline {B_1(0)})\ ? $$ , because the Hoelder space is a vector space .
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what happened to $k?$ – zhw. Sep 08 '18 at 15:36
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oh , sorry I mean $$ l\in\mathbb{N} $$ – Matillo Sep 08 '18 at 16:11
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I think $$ x_1x_2\in C^{l,\alpha}(\overline {B_1(0)}) $$ for all $$ l\in \mathbb{N} \ and \ \alpha\in[0,1] . $$ – Matillo Sep 08 '18 at 16:37