Related papers: Carleman estimates and boundedness of associated m…

The main purpose of this paper is to prove H\"ormander's $L^p$-$L^q$ boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing Paley inequality and Hausdorff-Young-Paley inequality for…

In this paper we investigate $L^p$ and Sobolev boundedness of a certain class of pseudodifferential operators with non-regular symbols. We employ regularisation methods, namely convolution with a net of mollifiers $(\rho_\eps)_\eps$, and we…

We characterize the $L^p(\sigma)\to L^q(\omega)$ boundedness of positive dyadic operators of the form $ T(f\sigma)=\sum_{Q\in\mathscr{D}}\lambda_Q\int_Q f\,\mathrm{d}\sigma\cdot 1_Q, $ and the $L^{p_1}(\sigma_1)\times L^{p_2}(\sigma_2)\to…

In this paper we investigate the $L^p$-boundedness of certain classes of periodic pseudo-differential operators. The operators considered arise from the study of symbols on $\mathbb{T}^n\times\mathbb{Z}^n$ with limited regularity.

We analyze the spectrum of the operator $\Delta^{-1} [\nabla \cdot (K\nabla u)]$, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral…

Housdorff-Young's inequality establishes the boundedness of the Fourier transform from $L^p$ to $L^q$ spaces for $1\leq p\leq2$ and $q=p'$, where $p'$ denotes the Lebesgue-conjugate exponent of $p$. This paper extends this classical result…

The aim of this paper is to introduce a generalization of the (p,q)-Bleimann-Butzer-Hahn operators based on (p,q)-integers and obtain Korovkin's type statistical approximation theorem for these operators. Also, we establish the rate of…

We establish optimal L^p bounds for the nontangential maximal function of the gradient of the solution to a second order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the…

By using some deep tools from microlocal analysis, the authors of the papers (Ann. of Math., 165 (2007), 567--591, J. Amer. Math. Soc., 23 (2010), 655--691; Invent. Math., 178 (2009), 119--171; Duke Math. J., 158(2011), 83--120) have…

We show that multipliers of second order Riesz transforms on products of discrete abelian groups enjoy the $L^{p} $ estimate $p^{\ast} -1$, where $p^{\ast} = \max \{ p,q \}$ and $p$ and $q$ are conjugate exponents. This estimate is sharp if…

For indices p and q, 1 < p <= q < infini and a linear operator L satisfying some weak-type boundedness conditions on suitable function spaces, we give in the Dunkl setting sufficient conditions on nonnegative pairs of weight functions to…

Let $(\cx,\,d,\,\mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors show that for the maximal Calder\'on-Zygmund operator associated with a…

We consider here pseudo-differential operators whose symbol $\sigma(x,\xi)$ is not infinitely smooth with respect to $x$. Decomposing such symbols into four -sometimes five- components and using tools of paradifferential calculus, we derive…

In the theory of singular integral operators significant effort is often required to rigorously define such an operator. This is due to the fact that the kernels of such operators are not locally integrable on the diagonal, so the integral…

Given a complex, elliptic coefficient function we investigate for which values of $p$ the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly…

We prove uniform $L^p$ estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding resul of [3] in the case of Laplace-- Beltrami operators on…

In this note we are concerned with estimates for the spectral projection operator $\mathcal{P}_\mu$ associated with the twisted Laplacian $L$. We completely characterize the optimal bounds on the operator norm of $\mathcal{P}_\mu$ from…

The aim of this article is to study the $L^{p}$-boundedness of pseudo-differential operators on a homogeneous tree $ \mathfrak{X} $. For $p\in (1,2)$, we establish a connection between the $L^{p}$-boundedness of the pseudo-differential…

We prove $L^p$ estimates for the Bi-Carleson operator, which is a natural hybrid of the Carleson maximal operator and the bilinear Hilbert transform. The methods used are essentially based on the treatment of the Walsh analogue of the…

We investigate the $L_p \mapsto L_q$ boundedness of the Fourier multipliers. We obtain sufficient conditions, namely, we derive Hormander and Lizorkin type theorems. We also obtain the necessary conditions. For $M$-generalized monotone…