Related papers: Sharp Bounds for Oscillatory Integral Operators wi…

In this paper we establish sharp estimates (up to logarithmic losses) for the multilinear oscillatory integral operator studied by Phong, Stein, and Sturm and Carbery and Wright on any product $\prod_{j=1}^d L^{p_j}(\mathbb R)$ with each…

In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating Robin boundary condition. We establish the qualitative homogenization theorem on any Lipschitz domains satisfying a non-resonance…

We consider the Bochner-Schr\"odinger operator $H_{p}=\frac 1p\Delta^{L^p}+V$ on tensor powers $L^p$ of a Hermitian line bundle $L$ on a Riemannian manifold $X$ of bounded geometry under the assumption of non-degeneracy of the curvature…

We consider the problem on uniform estimates for an oscillatory integrals with the smooth phase functions having singularities $D_{\infty} $. The estimate is sharp and analogy to estimates of the work of V.N.Karpushkin.

Given a compact Lie group $G$, in this paper we establish $L^p$-bounds for pseudo-differential operators in $L^p(G)$. The criteria here are given in terms of the concept of matrix symbols defined on the non-commutative analogue of the phase…

In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of $L^2 \mapsto L^2$ type for the operator, as well as for the corresponding maximal function. If…

We prove uniform $L^p$ bounds for multilinear operators which are given by multipliers whose symbols are singular on a one dimensional subspace. The novelty is that these bounds are uniform in the choice of the subspace.

We provide the sharp $C^0$ estimate for the quaternionic Monge-Ampere equation on any hyperhermitian manifold. This improves previously known results concerning this estimate in two directions. Namely, it turns out that the estimate depends…

In this article we prove a sharp decay estimate for certain multilinear oscillatory integral operators of a form inspired by the general framework of Christ, Li, Tao, and Thiele [6]. A key purpose of this work is to determine when such…

We investigate the Hilbert transform and the maximal operator along a class of variable non-flat polynomial curves $(P(t),u(x)t)$ with measurable $u(x)$, and prove uniform $L^p$ estimates for $1<p<\infty$. In particular, via the change of…

We obtain sharp estimates for certain trilinear oscillatory integrals. In particular, we extend Phong and Stein's seminal result to a trilinear setting. This result partially answers a question raised by Christ, Li, Tao and Thiele…

We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on $(x_1 \partial_{x_1} f(x) ,..., x_n \partial_{x_n}f(x))$, where $f(x)$ is the phase function. We prove a theorem which provides estimates…

In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),\gamma_\alpha)$ to $L^1((0,\infty),\gamma_\alpha)$ and also from $L^\infty((0,\infty),\gamma_\alpha)$ to…

In this paper, we establish gradient bounds for $p(\cdot)$-harmonic differential forms subject to a Coulomb-type gauge condition. For variable exponents satisfying the log-H\"older continuity assumption, we derive higher integrability…

Using some resolution of singularities and oscillatory integral methods in conjunction with appropriate damping and interpolation techniques, L^p boundedness theorems for p > 2 are obtained for maximal operators over a wide range of…

Let $K$ be a standard H\"older continuous Calder\'on--Zygmund kernel on $\mathbb{R}^{\mathbf{d}}$ whose truncations define $L^2$ bounded operators. We show that the maximal operator obtained by modulating $K$ by polynomial phases of a fixed…

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 +…

In this paper we will define and investigate the imaginary powers $\left(-\triangle_{k,1}\right)^{-i\sigma},\sigma\in\mathbb{R}$ of the $(k,1)$-generalized harmonic oscillator $-\triangle_{k,1}=-\left\|x\right\|\triangle_k+\left\|x\right\|$…

We study semilinear rough stochastic partial differential equations as introduced in [Gerasimovi{\v{c}}s, Hairer; EJP 2019]. We provide $\mathcal{L}^p(\Omega)$-integrable a priori bounds for the solution and its linearization in case the…

In this paper we prove the sharp boundedness for a fractional type operator given by a kernel that satisfy a $L^{\alpha,r'}$-H\"ormander conditions and a fractional size condition, where $0<\alpha<n$ and $1< r'\leq \infty$. To prove this…