... explained below, and theextension will be denoted by sinp.Definesinpon πp/2,πp by sinptwπp− t. Then,we define sinpon −πp, 0 such that sinpis an odd function. Finally, ... Finally, we extend sinpto R by2πp-periodicity. It is not difficult to verify that sinphas the following properties:i sinp00, sinp01;iip − 1|sinpt|p |sinpt|p ... αqp1ωpr4/p−22/plsinlpθsin2pθ,P2t, θ, rqp1ωpr−2/qsinpθFr2/psinpθ, tΦqr2/qΦpω sinpθqp1ωpr−2/qsinpθer2/psinpθ, t,2.12withθ...