ﻻ يوجد ملخص باللغة العربية
Let Pd denote the space of all real polynomials of degree at most d. It is an old result of Stein and Wainger that for every polynomial P in Pd: |p.v.int_R {e^{iP(t)} dt/t} | < C(d) for some constant C(d) depending only on d. On the other hand, Carbery, Wainger and Wright claim that the true order of magnitude of the above principal value integral is log d. We prove this conjecture.
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the associated fr
We provide elementary proofs for the terms that are left in the work of Kelly Bickel, Sandra Pott, Maria C. Reguera, Eric T. Sawyer, Brett D. Wick who proved the sharp weighted $A_2$ bound for Haar shifts and Haar multiplier. Our proofs use weighted
In this paper, we prove $L^p$ decay estimates for multilinear oscillatory integrals in $mathbb{R}^2$, establishing sharpness through a scaling argument. The result in this paper is a generalization of the previous work by Gressman and Xiao (2016).
We propose a new method of estimating oscillatory integrals, which we call a stationary set method. We use it to obtain the sharp convergence exponents of Tarrys problems in dimension two for every degree $kge 2$. As a consequence, we obtain sharp Fo
For $m, d in {mathbb N}$, a jittered sampling point set $P$ having $N = m^d$ points in $[0,1)^d$ is constructed by partitioning the unit cube $[0,1)^d$ into $m^d$ axis-aligned cubes of equal size and then placing one point independently and uniformly