Some Inequalities for Entire Functions
Some Inequalities for Entire Functions
For any entire functions $\varphi (z)$ and $\psi (z)$ on C with finite norm \[ {\left \{ {\frac {1}{\pi }\int {\int \limits _{\mathbf {C}} {|f(z){|^2}\exp ( - |z{|^2})dx\;dy} } } \right \}^{1/2}} < \infty ,\] we show that the inequality \[ \begin {array}{*{20}{c}} {\frac {2}{\pi }\int {\int \limits _{\mathbf {C}} …