Related papers: Bounds on oscillatory integral operators based on …
In this paper we prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted $L^p$…
In this paper we consider a generalized version of bounded oscillation operators, involving new parameters in the definition, as well as considering the operators on vector-valued function spaces. With this definition we will capture some…
We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator,…
In this paper, we shall prove the uniform sharp $L^p$ decay estimates for a class of oscillatory integral operators with polynomial phases. By this one-dimensional result, we can use the rotation method to obtain uniform sharp $L^p$…
In 2005, Li, Tao, Thiele and the author raised a general question concerning upper bounds for a class of multilinear oscillatory integral operators, and established such bounds in a few cases. Most cases remain open. The present paper is…
In this paper, we consider $L^p$- estimate for a class of oscillatory integral operators satisfying the Carleson-Sj\"olin conditions with further convex and straight assumptions. As applications, the multiplier problem related to a general…
We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of oscillatory Riemann-Hilbert problems associated with partial…
Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. Lebesgue space norm inequalities are established for multilinear integral operators of Calderon-Zygmund type which…
We investigate the boundedness of oscillating singular integrals on Lie groups of polynomial growth in order to extend the classical oscillating conditions due to Fefferman and Stein for the boundedness of oscillating convolution operators.…
We investigate $(2+1)-$dimensional oscillatory integral operators characterized by polynomial phase functions. By employing Stein's complex interpolation, we derive sharp $L^2\to L^p$ decay estimates for these operators.
We will explain how to compute the exact $L^p$ operator norm of a "quadratic perturbation" of the real part of the Ahlfors--Beurling operator. For the lower bound estimate we use a new approach of constructing a sequence of laminates…
This thesis is devoted to asymptotic norm estimates for oscillatory integral operators acting on the L^2 space of functions of one real variable. The operators in question have compact support and an oscillatory kernel of the form exp(i…
Oscillatory integrals arise in many situations where it is important to obtain decay estimates which are stable under certain perturbations of the phase. Examining the structural problems underpinning these estimates leads one to consider…
We obtain two-weighted $L^2$ norm inequalities for oscillatory integral operators of convolution type on the line whose phases are of finite type. The conditions imposed on the weights involve geometrically-defined maximal functions, and…
We consider the following oscillatory integral operator \begin{equation}\label{opera-defi-1} T_{\alpha,m}f(x)=\int_{\mathbb R^n}e^{i(x_1^{\alpha_1} y_1^m+\cdots+x_n^{\alpha_n} y_n^m)}f(y)dy, \end{equation} where the function $f$ is a…
In this paper, we estimate an operator norm of dilation operators on block spaces ($\mathfrak{B}_{r,\alpha}(\mathbb{Q}_p)$) over $p$-adic field. With this estimate, we establish the boundedness of $p$-adic Hardy-Hilbert type integral…
We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter H\"ormander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots +…
We revisit the multilinear Kakeya, curved Kakeya, restriction, and oscillatory integral estimates that were obtained in paper of Bennett, Carbery, and the author using a heat flow monotonicity method applied to a fractional Cartesian…
This paper mainly dedicates to prove a plethora of weighted estimates on Morrey spaces for bilinear fractional integral operators and their general commutators with BMO functions of the form…
We study the boundedness of some sublinear operators on weighted Morrey spaces under certain size conditions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator,…