A General Norm on Extension of a Hilbert’s Type Linear Operator

The main purpose of this paper is to study a general norm on extension of a Hilbert’s type linear operator in the continuous and discrete form. In addition to expressing the norm of a Hilbert’s type linear operator T : L2(0,1) ! L2(0,1), a more general case with  > 0, for the continuous form has been studied. By putting  = 1 a norm of extension of Hilbert’s integral linear operator is obtained. Similar results have been expressed for series when 0 <  6 2.