An improved bound on the sum-product estimate in ${\mathbb{F}}_p$

We give an improved bound on the famed sum-product estimate in a field of residue class modulo $p$ (${\mathbb{F}}_p$) by Erd\H{o}s and Szemeredi, and a non-empty set $A\subset {\mathbb{F}}_p$ such that: $$\max \{\mathrm{\mid }A+A\mathrm{\mid },\mathrm{\mid }AA\mathrm{\mid }\}\gg \min \{\frac{\mathrm{\mid }A{\mathrm{\mid }}^{15\mathrm{/}14}\max \{1,\mathrm{\mid }A{\mathrm{\mid }}^{1\mathrm{/}7}{p}^{-1\mathrm{/}14}\}}{(\log \mathrm{\mid }A\mathrm{\mid }{)}^{2\mathrm{/}7}},\frac{\mathrm{\mid }A{\mathrm{\mid }}^{11\mathrm{/}12}{p}^{1\mathrm{/}12}}{(\log \mathrm{\mid }A\mathrm{\mid }{)}^{1\mathrm{/}3}}\},$$ and more importantly: $$\max \{\mathrm{\mid }A+A\mathrm{\mid },\mathrm{\mid }AA\mathrm{\mid }\}\gg \frac{\mathrm{\mid }A{\mathrm{\mid }}^{15\mathrm{/}14}}{(\log \mathrm{\mid }A\mathrm{\mid }{)}^{2\mathrm{/}7}}\mathrm{.}$$