Boundedness of oscillatory singular integrals

This thesis consists of four chapters. In the first chapter, basic concepts and fundamental theorems which we will use in second, third and fourth chapters. In the second chapter, we consider the oscillatory singular integralTf(x)=?_(R^n)? ? e^(i.P(x,y) ) K(x-y)f(y)dy (1) ? .We studied the boundedness of this oscillatory singular integrals with homogeneous smooth kernels. So first, the (L^p,L^p )-boundedness and (L^1,L^1 )-boundedness of Oscillatory singular integrals with homogeneous smooth kernels is examined.In the third chapter, we take up oscillatory singular integrals with rough kernels and the boundedness of this oscillatory singular integrals is studied and we study boundedness of this integrals.In the fourth chapter, we take up Oscillatory singular integrals with standart kernels and the boundedness of this oscillatory singular integrals is studied and we study boundedness of this integrals.