Related papers: $L^{p}$ estimates for multi-linear and multi-param…

We prove L^p estimates for a large class of multi-linear operators, which includes the multi-linear paraproducts studied by Coifman and Meyer, as well as the bilinear Hilbert transform.

In this work we obtain sharp $L^p$-estimates for pseudo-differential operators on arbitrary graded Lie groups. The results are presented within the setting of the global symbolic calculus on graded Lie groups by using the Fourier analysis…

Analogues of multi-paramter multiplier operators on R^d are defined on the torus T^d. It is shown that these operators satisfy the classical Coifman-Meyer theorem. In addition, L log L and L (log L)^n end-point estimates are proved.

We prove $L^p$ estimates for various multi-parameter bi- and trilinear operators with symbols acting on fibers of the two-dimensional functions. In particular, this yields estimates for the general bi-parameter form of the twisted…

We consider bilinear multipliers that appeared as a distinguished particular case in the classification of two-dimensional bilinear Hilbert transforms by Demeter and Thiele [9]. In this note we investigate their boundedness on Sobolev…

For multiparameter bilinear paraproduct operators $B$ we prove the estimate $$ B: L^p X L^q --> L^r, 1<p,q\le{}\infty. $$ Here, $1/p+1/q=1/r$ and special attention is paid to the case of $0<r<1$. (Note that the families of multiparameter…

C. Muscalu, J. Pipher, T. Tao and C. Thiele proved in \cite{MPTT1} that the standard bilinear and bi-parameter Hilbert transform does not satisfy any $L^{p}$ estimates. They also raised a question asking if a bilinear and bi-parameter…

In this paper we prove $L^p$-estimates for H\"ormander classes of pseudo-differential operators on the torus $\mathbb{T}^n$. The results are presented in the context of the global symbolic calculus of Ruzhansky and Turunen on…

In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on $L^p$-spaces. First, we prove…

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.

The main purpose of this paper is to study $L^r$ H\"older type estimates for a bi-parameter trilinear Fourier multiplier with flag singularity, and the analogous pseudo-differential operator, when the symbols are in a certain product form.…

In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space…

In this paper we establish the $L^p$-$L^q$ estimates for global pseudo-differential operators on graded Lie groups. We provide both necessary and sufficient conditions for the $L^p$-$L^q$ boundedness of pseudo-differential operators…

Muscalu, Tao, and Thiele prove $L^p$ estimates for the "Biest" operator defined on Schwartz functions by the map \begin{align*} \hspace{5mm} C^{1,1,1}:& (f_1, f_2, f_3) \mapsto \int_{\xi_1 < \xi_2< \xi_3} \left[ \prod_{j=1}^3 \hat{f}_j…

In this article, we investigate the multilinear distorted multiplier estimate (Coifman-Meyer type theorem) associated with the Schr\"{o}dinger operator $H=-\Delta + V$ in the framework of the corresponding distorted Fourier transform. Our…

We prove L^p estimates for a two-dimensional bilinear operator of paraproduct type. This result answers a question posed by Demeter and Thiele in [3].

We show results on $L^p$-spectral multipliers for Maxwell operators with bounded measurable coefficients. We also present similar results for the Stokes operator with Hodge boundary conditions and the Lam\'e system. Here we rely on…

In this paper we continue our program of revisiting the new aspects about the boundedness properties of pseudo-differential operators on the torus. Here we prove $H^p$-$L^p$ and $H^p$-estimates for H\"ormander classes of pseudo-differential…

We develop a general framework for the analysis of operator-valued multilinear multipliers acting on Banach-valued functions. Our main result is a Coifman-Meyer type theorem for operator-valued multilinear multipliers acting on suitable…

We develop a set of $L^{p}$ estimates for functions $u$ that are a joint quasimodes (approximate eigenfunctions) of $r$ semiclassical pseudodifferential operators $p_{1}(x,hD),\dots,p_{r}(x,hD)$. This work extends Sarnak and Marshall's work…