Let f be holomorphic in a neighborhood of \(D _ { r } ( z _ { 0 } )\) . Show that for any \(s < r ,\) , there exists a constant \(c > 0\) such that
\[ \| f \| _ { ( \infty , s ) } \leq c \| f \| _ { ( 1 , r ) } , \]
where \(\| f \| _ { ( \infty , s ) } = \operatorname* { s u p } _ { z \in D _ { s } ( z _ { 0 } ) } | f ( z ) | { \mathrm { ~ a n d ~ } } \| f \| _ { ( 1 , r ) } = \int _ { D _ { r } ( z _ { 0 } ) } | f ( z ) | d x d y .\)