Related papers: Multipliers for spherical harmonic expansions
We give a simple necessary and sufficient condition for maximal operators associated with radial Fourier multipliers to be bounded on $L^p_{rad}$ and $L^p$ for certain $p$ greater than $2$. The range of exponents obtained for the…
We study the boundedness of Toeplitz-type operators defined in the context of the Calder\'on reproducing formula considering the specific wavelets whose Fourier transforms are related to Laguerre polynomials. Some sufficient conditions for…
In this paper it is proposed a very simple method for estimating the maximal operator in $L_1$. Using this method one can considerably improve the existing theorems on convergence almost-everywhere of eigenfunction expansions of an…
In this paper, we establish an operator-valued Fourier multiplier theorem in weighted Lebesgue spaces, Besov and Triebel--Lizorkin spaces, assuming the multiplier has $\mathcal{R}$-bounded range and satisfies an $\ell^r$-summability…
We prove sharp uniform $L^p$-bounds for low-lying eigenfunctions of non-self-adjoint semiclassical pseudodifferential operators $P$ on $\mathbb{R}^{n}$ whose principal symbols are doubly-characteristic at the origin of $\mathbb{R}^{2n}$.…
In this work we investigate the boundedness of Fourier multipliers on Triebel-Lizorkin spaces associated to positive Rockland operators on a graded Lie group. The found criterion is expressed in terms of the H\"ormander-Mihlin condition on…
Consider the linear space of functions on the binary hypercube and the linear operator $S_\delta$ acting by averaging a function over a Hamming sphere of radius $\delta n$ around every point. It is shown that this operator has a…
We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on…
In this paper, we investigate the $H^p(G) \rightarrow L^p(G)$, $0< p \leq 1$, boundedness of multiplier operators defined via group Fourier transform on a graded Lie group $G$, where $H^p(G)$ is the Hardy space on $G$. Our main result…
In this paper, we study the $L^p$ boundedness of a class of oscillating multiplier operator for the Dunkl transform, $T_{m_\alpha}=\mathcal{F}_k^{-1}(m_{\alpha}\mathcal{F}_k(f))$ with $m(\xi)=|\xi|^{-\alpha}e^{\pm i|\xi|}\phi(\xi)$. We…
In this work sufficient conditions on the order of the symbol are developed to ensure boundedness, compactness and r-nuclearity of pseudo-differential operators in $\hbar\mathbb{Z}^n$. In addition, these conditions allow us to obtain growth…
We obtain a characterization of ${\mathcal S}^{\{M_p\}}_{\{M_p\}}(\mathbb R^n)$ and $\mathcal {S}^{(M_p)}_{(M_p)}(\mathbb {R}^n)$, the general Gelfand-Shilov spaces of ultradifferentiable functions of Roumieu and Beurling type, in terms of…
In this paper we consider Fourier multiplier operators between vector-valued Besov spaces with different integrability exponents $p$ and $q$, which depend on the type $p$ and cotype $q$ of the underlying Banach spaces. In a previous paper…
In this work we give H\"older-Besov estimates for periodic Fourier multipliers. We present a class of bounded pseudo-differential operators on periodic Besov spaces with symbols of limited regularity.
We present a general framework of localized operators, i.e., operators whose matrix coefficients with respect to the Gabor frame are concentrated on the diagonal. We show that localized operators are bounded between modulation spaces, and…
We consider harmonic Toeplitz operators $T_V = PV:{\mathcal H}(\Omega) \to {\mathcal H}(\Omega)$ where $P: L^2(\Omega) \to {\mathcal H}(\Omega)$ is the orthogonal projection onto ${\mathcal H}(\Omega) = \left\{u \in L^2(\Omega)\,|\,\Delta u…
In this paper, we enlarge the space of uniformly supported pseudo-differential operators on some groupoids by considering kernels satisfying certain asymptotic estimates. We show that such enlarged space contains the compact parametrix, and…
Quantization and spectral properties of Toeplitz operators acting on spaces of pluriharmonic functions over bounded symmetric domains and $\mathbb C^n$ are discussed. Results are presented on the asymptotics \begin{align*} \|…
This paper studies the "energy space" $\mathcal{H}_{\mathcal{E}}$ (the Hilbert space of functions of finite energy, aka the Dirichlet-finite functions) on an infinite network (weighted connected graph), from the point of view of the…
In a recent work, P. Chen and E. M. Ouhabaz proved a $p$-specific $L^p$-spectral multiplier theorem for the Grushin operator acting on $\mathbb{R}^{d_1}\times\mathbb{R}^{d_2}$ which is given by \[ L =-\sum_{j=1}^{d_1} \partial_{x_j}^2 -…