Related papers: Logarithmic oscillatory multipliers and log-subdya…

Through the study of novel variants of the classical Littlewood-Paley-Stein $g$-functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on $\mathbb{R}^d$ satisfying regularity hypotheses adapted to…

We provide characterizations for boundedness of multilinear Fourier operators on Hardy-Lebesgue spaces with symbols locally in Sobolev spaces. Let $H^q(\mathbb R^n)$ denote the Hardy space when $0<q\le 1$ and the Lebesgue space $L^q(\mathbb…

We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger ; this extends the…

Let $\sigma(x,\xi) $ be a sufficiently regular function defined on $R^d \times R^d.$ The pseudo-differential operator with symbol $\sigma$ is defined on the Schwartz class by the formula: \[f\to\sigma f(x)=\int_{R^d} \sigma(x,\xi)…

Bilinear Fourier multipliers of the form $e^{i (|\xi| + |\eta|+ |\xi + \eta|)} \sigma (\xi, \eta)$ are considered. It is proved that if $\sigma (\xi, \eta)$ is in the H\"ormander class $S^{m}_{1,0} (\mathbb{R}^{2n})$ with $m=-(n+1)/2$ then…

We establish certain square function estimates for a class of oscillatory integral operators with homogeneous phase functions. These results are employed to deduce a refinement of a previous result of Mockenhaupt Seeger and Sogge…

We show that a bilinear radial Fourier multiplier operator with symbol $\sigma$ is $L^2(\R^n)\times L^2(\R^n) \to L^1(\R^n)$ bounded, $n\in \mathbb N,$ if the function $\sigma$ satisfies the smoothness condition $\sigma(2^j\cdot)\Phi\in…

Fourier multiplier analysis is developed for nonlocal peridynamic-type Laplace operators, which are defined for scalar fields in $\mathbb{R}^n$. The Fourier multipliers are given through an integral representation. We show that the integral…

For $s > 0$, $s \neq 1$, bilinear Fourier multipliers of the form $e^{i (|\xi|^s + |\eta|^s+ |\xi + \eta|^s)} \sigma (\xi, \eta)$ are considered, where $\sigma(\xi, \eta)$ belongs to the H\"ormander class $S^{m}_{1, 0}(\mathbb{R}^{2n})$. A…

In this paper we study the $L^p$-$L^q$ boundedness of the Fourier multipliers in the setting where the underlying Fourier analysis is introduced with respect to the eigenfunctions of an anharmonic oscillator $A$. Using the notion of a…

In this paper we develop the theory of Fourier multiplier operators $T_{m}:L^{p}(\mathbb{R}^{d};X)\to L^{q}(\mathbb{R}^{d};Y)$, for Banach spaces $X$ and $Y$, $1\leq p\leq q\leq \infty$ and $m:\mathbb{R}^d\to \mathcal{L}(X,Y)$ an…

In this note, we deal with the fractional Logarithmic Schr\"{o}dinger operator $(I+(-\Delta)^s)^{\log}$ and the corresponding energy spaces for variational study. The fractional (relativistic) Logarithmic Schr\"{o}dinger operator is the…

For any bounded, regulated function $m: [0,\infty) \to \mathbb{C}$, consider the family of operators $\{ T_R \}$ on the sphere $S^d$ such that $T_R f = m(k/R) f$ for any spherical harmonic $f$ of degree $k$. We completely characterize the…

We find that if a Fourier multiplier is continuous from $L^{\Phi_1}$ to $L^{\Phi_2}$, then it is also continuous from $M^{\Phi_1,\Psi}$ to $M^{\Phi_2,\Psi}$, where $\Phi_1,\Phi_2,\Psi$ are quasi-Young functions and $\Phi_1$ fulfills the…

Multi-norm singular integrals and Fourier multipliers were introduced in [29], and one application of these notions was a precise description of the composition of convolution operators with Calder\'on-Zygmund kernels adapted to $n$…

The paper focuses on the behaviour of unimodular Fourier multipliers with exponential growth in the context of weighted $L^p$-spaces. Our main result shows that much of the general theory of multipliers is approachable through the theory of…

We establish precise regularity conditions for $L_p$-boundedness of Fourier multipliers in the group algebra of $SL_n(\mathbf{R})$. Our main result is inspired by H\"ormander-Mikhlin criterion from classical harmonic analysis, although it…

In this note we study the $L^p-L^q$ boundedness of Fourier multipliers of anharmonic oscillators, and as a consequence also of spectral multipliers, for the range $1<p \leq 2 \leq q <\infty$. The underlying Fourier analysis is associated…

We study the high-frequency Fourier asymptotics of imaginary Gaussian multiplicative chaos on the unit circle, a complex-valued random distribution formally given by $\mathrm M_{\mathrm i\beta}=\exp(\mathrm i\beta X)$, where $X$ is a…

A classical theorem of Mihlin yields Lp estimates for spectral multipliers Lp(R^d) -> Lp(R^d); g -> F^{-1}[f(| |^2) Fg] in terms of L^\infty bounds of the multiplier function f and its weighted derivatives up to an order > d/2. This…