In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the f...In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ（R＋） for γ 〉 1 and the sphere function ΩεFβ（S^n-1） for someβ 〉 0 which is distinct from HI（Sn-1）.展开更多
The integral g(x)e(f(x))dx is discussed, where g(x) denotes a smooth function. Theresult is an estimate to this integral with a sharp remainder term. This can be used in estimating exponential sums as in the theory of...The integral g(x)e(f(x))dx is discussed, where g(x) denotes a smooth function. Theresult is an estimate to this integral with a sharp remainder term. This can be used in estimating exponential sums as in the theory of exponential pairs.展开更多
基金Supported by the National Natural Science Foundation of China(11071200,11371295)
文摘In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ（R＋） for γ 〉 1 and the sphere function ΩεFβ（S^n-1） for someβ 〉 0 which is distinct from HI（Sn-1）.
基金Project supported by the National Natural Science Foundation of China.
文摘The integral g(x)e(f(x))dx is discussed, where g(x) denotes a smooth function. Theresult is an estimate to this integral with a sharp remainder term. This can be used in estimating exponential sums as in the theory of exponential pairs.
