Related papers: Multiplier theorems via martingale transforms

We give a purely combinatorial proof for a two-fold generalization of van der Waerden-Brauer's theorem and Hindman's theorem. We also give tower bounds for a finite version of it.

Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms…

In a first part, we give a new proof of Koenigs theorem and, in a second part, we determine the local form of all the superintegrable Riemannian Liouville metrics as well as their global geometries.

We prove Penner's theorem on horocycles and theorems of Ptolemy and Casey, all with full converses, in hyperbolic space of several dimensions. Recently Waddle observed that the equations underpinning these three theorems are related, and it…

In this paper, we establish some general Kastler-Kalau-Walze type theorems for any dimensional manifolds with boundary which generalize the results in [WW1].

Given a fixed $p\neq 2$, we prove a simple and effective characterization of all radial multipliers of $\cF L^p(\Bbb R^d)$, provided that the dimension $d$ is sufficiently large. The method also yields new $L^q$ space-time regularity…

We show that Riesz transforms associated to the Grushin operator G = -\Delta - |x|^2\partial_t^2 are bounded on L^p(R^n+1). We also establish an analogue of H\"ormander-Mihlin multiplier theorem and study Bochner-Riesz means associated to…

We prove an $L^p$-spectral multiplier theorem under the sharp regularity condition $s > d\left|1/p - 1/2\right|$ for sub-Laplacians on M\'etivier groups. The proof is based on a restriction type estimate which, at first sight, seems to be…

A new technique for proving uniqueness of martingale problems is introduced. The method is illustrated in the context of elliptic diffusions in $R^d$.

In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method of multipliers encounters troubles in both…

In this paper we consider a multiparametric version of Wolfgang Schmidt and Leonard Summerer's parametric geometry of numbers. We apply this approach in two settings: the first one concerns weighted Diophantine approximation, the second one…

The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…

We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

A vector-valued version of the Girsanov theorem is presented, for a scalar process with respect to a Banach-valued measure. Previously, a short discussion about the Birkhoff-type integration is outlined, as for example integration by…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

We prove a H\"{o}rmander type multiplier theorem for multilinear Fourier multipiers with multiple weights. We also give weighted estimates for their commutators with vector $BMO$ functions.

We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The…

Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and, naturally, mathematics. In a general setting they can be described as frame multipliers, consisting of analysis, multiplication by…

We consider some versions and generalizations of an approach to the expansion of iterated Ito stochastic integrals of arbitrary multiplicity $k$ $(k\in\mathbb{N})$ based on generalized multiple Fourier series. Expansions of iterated…