I don't know the meaning of these:

1) $\displaystyle sup_{B_\delta}|f(x,y)| $

Where $\displaystyle B_\delta $ is the ball of radius $\displaystyle \delta$.

2) $\displaystyle \int \int _{R^2 \B_{\delta}} f(xy)dxdy$

I don't know what is $\displaystyle R^2 \B_{\delta}$

Please read my Latex because the symbol really don't show correctly.