$L^2$ Estimates for Oscillatory Integrals
نویسندگان
چکیده
منابع مشابه
Homogeneous Estimates for Oscillatory Integrals
Abstract. Let u(x, t) be the solution to the free time-dependent Schrödinger equation at the point (x, t) in space-time Rn+1 with initial data f . We characterize the size of u in terms Lp(Lq)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces Ḣs (Rn). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interp...
متن کاملUniform estimates for cubic oscillatory integrals
This paper establishes the optimal decay rate for scalar oscillatory integrals in n variables which satisfy a nondegeneracy condition on the third derivatives. The estimates proved are stable under small linear perturbations, as encountered when computing the Fourier transform of surface-carried measures. The main idea of the proof is to construct a nonisotropic family of balls which locally ca...
متن کاملWeighted estimates for rough oscillatory singular integrals
Sn−1 Ω = 0. The radial factor h has bounded variation. The necessary condition on the weight is similar to the Ap condition but involves rectangles (instead of cubes) arising from a covering of a star-shaped set related to Ω. AMS Mathematics Subject Classification: 42B20
متن کاملCertain Estimates of Oscillatory Integrals and Extrapolation
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, B...
متن کاملOscillatory Integrals and L Estimates for Schrödinger Equations
This paper is concerned with Schrödinger equations whose principal operators are elliptic. Under certain degenerate condition we show the estimate of an oscillatory integral related to the solution operator in free case, and then employ fractionally integrated groups to obtain the Lp estimate of solutions for the initial data belonging to a dense subspace of Lp in the case of integrable potenti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1998
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-76-2-201-211