Certain Estimates of Oscillatory Integrals and Extrapolation
نویسنده
چکیده
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 L boundedness for these oscillatory integrals under rather weak size conditions on the kernel function. Keywords—Fourier transform, oscillatory integrals, Orlicz spaces, Block spaces, Extrapolation, L boundedness.
منابع مشابه
The Numerical Evaluation of Very Oscillatory Infinite Integrals by Extrapolation
Recently the author has given two modifications of a nonlinear extrapolation method due to Levin and Sidi, which enable one to accurately and economically compute certain infinite integrals whose integrands have a simple oscillatory behavior at infinity. In this work these modifications are extended to cover the case of very oscillatory infinite integrals whose integrands have a complicated and...
متن کاملThe Numerical Evaluation of Very Oscillatory Infinite Integrals
Recently the author has given two modifications of a nonlinear extrapolation method due to Levin and Sidi, which enable one to accurately and economically compute certain infinite integrals whose integrands have a simple oscillatory behavior at infinity. In this work these modifications are extended to cover the case of very oscillatory infinite integrals whose integrands have a complicated and...
متن کاملar X iv : 0 70 4 . 15 37 v 1 [ m at h . C A ] 1 2 A pr 2 00 7 ESTIMATES FOR SINGULAR INTEGRALS AND EXTRAPOLATION
In this note, we study singular integrals with rough kernels, which belong to a class of singular Radon transforms. We prove certain estimates for the singular integrals that are useful in an extrapolation argument. As an application, we prove L p boundedness of the singular integrals under a certain sharp size condition on their kernels.
متن کاملExtrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability
In a recent work by the author an extrapolation method, the W-transformation, was developed, by which a large class of oscillatory infinite integrals can be computed very efficiently. The results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper. It is shown in particular that these divergent integrals exist in the sense of Abel summability an...
متن کاملExtrapolation Methods for Oscillatory Infinite Integrals
The non-linear transformations for accelerating the convergence of slowly convergent infinite integrals due to Levin & Sidi (1975) are modified in two ways. These modifications enable one to eval uate accurately some oscillatory infinite integrals with less work. Special emphasis is placed on the evaluation of Fourier and Hankel transforms and some simple algorithms for them are given. Converge...
متن کامل