Related papers: $L^p$ estimates for an oscillating Dunkl multiplie…

We prove $L^{p}$-boundedness of oscillating multipliers on all symmetric spaces and a class of locally symmetric spaces.

Let ${\frak M}^\alpha$ be the spherical maximal operators of complex order $\alpha$ on ${\mathbb R^n}$. In this article we show that when $n\geq 2$, suppose \begin{eqnarray*} \|{\frak M}^{\alpha} f \|_{L^p({\mathbb R^n})} \leq C\|f…

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…

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…

Let $X$ be a complete, simply connected harmonic manifold with sectional curvatures $K$ satisfying $K \leq -1$. In \cite{biswas6}, a Fourier transform was defined for functions on $X$, and a Fourier inversion formula and Plancherel theorem…

Dunkl operators may be regarded as differential-difference operators parameterized by finite reflection groups and multiplicity functions. In this paper, the Littlewood--Paley square function for Dunkl heat flows in $\mathbb{R}^d$ is…

We prove endpoint bounds for the square function associated with radial Fourier multipliers acting on $L^{p}$ radial functions. This is a consequence of endpoint bounds for a corresponding square function for Hankel multipliers. We obtain a…

We prove $L^p$ bounds in the range $1<p<\infty$ for a maximal dyadic sum operator on $\rn$. This maximal operator provides a discrete multidimensional model of Carleson's operator. Its boundedness is obtained by a simple twist of the proof…

In this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on $\mathbb{R}^d$ isomorphic to $\mathbb{Z}^d_2$. We prove that imaginary powers of this operator are…

We prove that the existence of a Mihlin-H\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The…

In this paper, we study the spherical maximal operator $ M_E $ over $ E\subset [1,2]$, restricted to radial functions. In higher dimensions $ d\geq 3$, we establish a complete range of $ L^p-$improving estimates for $ M_E $. In two…

We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq…

We present a simple geometric approach to studying the $L^p$ boundedness properties of Stein's spherical maximal operator, which does not rely on the Fourier transform. Using this, we recover a weak form of Stein's spherical maximal…

In this paper, we investigate $L^p-$boundedness of the bilinear spherical maximal function associated with a general set $E\subset\R_+$. We quantify the range of $L^p-$boundedness in terms of a dilation-invariant notion of upper Minkowski…

We study a parametrized family of strong maximal fractional operators. We prove their $L^p$ to $L^q$ boundedness for $1<p\le q<\infty$.

In this article we investigate $L^p$ boundedness of the spherical maximal operator $\mathfrak{m}^\alpha$ of (complex) order $\alpha$ on the $n$-dimensional hyperbolic space $\mathbb{H}^n$, which was introduced and studied by El Kohen. We…

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…

We prove that the spherical mean value of the Dunkl-type generalized translation operator $\tau^y$ is a positive $L^p$-bounded generalized translation operator $T^t$. As application, we prove the Young inequality for a convolution defined…

The present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a…

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…