Related papers: On multipliers into martingale $SL^\infty$ spaces …

We present a class of weight functions $ w$ on the circle $ \mathbb{T}$, called L\'evy-Khinchin-Schoenberg (LKS) weights, for which we are able to completely characterize (in terms of a capacitary inequality) all Fourier multipliers for the…

In this note we introduce a new kind of augmentation of filtrations along a sequence of stopping times. This augmentation is suitable for the construction of new probability measures associated to a positive strict local martingale as done…

We study weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function (in the sense of Braun, Meise and Taylor) and a weight system. We characterize when such spaces are ultrabornological in terms of the defining…

We present two examples of loss of the predictable representation property for semi-martingales by enlargement of the reference filtration. First of all we show that the predictable representation property for a square-integrable…

In this paper, we study multilinear Fourier multiplier operators on Hardy spaces. In particular, we prove that the multilinear Fourier multiplier operator of H\"ormander type is bounded from $H^{p_1} \times \cdots \times H^{p_m}$ to $H^p$…

We examine how closely a multiplicative function resembles an additive function. Given a multiplicative function $g$ and an additive function $f$, we examine the size of the quantity $E(f,g;x)=\# \{n\leq x:f(n)=g(n)\}$. We establish a lower…

Let $f : \mathbf{N} \rightarrow \mathbf{C}$ be a bounded multiplicative function. Let $a$ be a fixed integer (say $a = 1$). Then $f$ is well-distributed on the progression $n \equiv a \pmod{q} \subset \{1,\dots, X\}$, for almost all primes…

We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p.

Let $(\Omega_1, \mathcal{F}_1, \mu_1)$ and $(\Omega_2, \mathcal{F}_2, \mu_2)$ be two measure spaces and let $1 \leq p,q \leq +\infty$. We give a definition of Schur multipliers on $\mathcal{B}(L^p(\Omega_1), L^q(\Omega_2))$ which extends…

In this paper we investigate the boundedness properties of bilinear multiplier operators associated with unimodular functions of the form $m(\xi,\eta)=e^{i \phi(\xi-\eta)}$. We prove that if $\phi$ is a $C^1(\mathbb R^n)$ real-valued…

For bilinear Fourier multipliers that contain some oscillatory factors, boundedness of the operators between Lebesgue spaces is given including endpoint cases. Sharpness of the result is also considered.

In this work a linearly constrained minimization of a positive semidefinite quadratic functional is examined. Our results are concerning infinite dimensional real Hilbert spaces, with a singular positive operator related to the functional,…

The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…

When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have singular paths. This phenomenon has…

Given Mikhlin-H\"ormander multipliers $m_i$, $i=1,..., N$, with uniform estimates we prove an optimal $\sqrt{\log(N+1)}$ bound in $L^p$ for the maximal function $\sup_i|\cF^{-1}[m_i\hat f]|$ and related bounds for maximal functions…

We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces $M^{\Phi,\varphi}_{w}({\mathbb R}^n)$. In all the cases, the conditions for the boundedness are given…

We consider Marcinkiewicz multipliers of any lacunary order defined by means of uniformly bounded variation on each lacunary Littlewood--Paley interval of some fixed order $\tau\geq 1$. We prove the optimal endpoint bounds for such…

Let $f$ be a real-valued $1$-bounded multiplicative function. Suppose that the mean-value of $f^{2}$ exists, and $$\int_{0}^{1} \Big | \sum_{n \leq N} f(n)e^{2\pi i n \alpha} \Big | d \alpha\leq N^{o(1)}$$ as $N \rightarrow \infty$, then…

We construct a class of Fourier multipliers whose associated operators are weak (1,1) bounded but fail to be weak (p, p) bounded for any 1 < p \leq \infty. Moreover, we show that this result is sharp.

For various $2\leq n,m \leq 6$, we propose some new algorithms for multiplying an $n\times m$ matrix with an $m \times 6$ matrix over a possibly noncommutative coefficient ring.