Abstract: We obtain appropriate sharp estimates for rough oscillatory integrals. Our results represent significant improvements as well as natural extensions of what was known previously.
Abstract: In this paper we study the boundedness properties of
certain oscillatory integrals with polynomial phase. We obtain sharp
estimates for these oscillatory integrals. By the virtue of these
estimates and extrapolation we obtain Lp boundedness for these
oscillatory integrals under rather weak size conditions on the kernel
function.
Abstract: A new nonlinear sum-difference inequality in two variables
which generalize some existing results and can be used as handy
tools in the analysis of certain partial difference equation is discussed.
An example to show boundedness of solutions of a difference value
problem is also given.