We study the Bochner-Riesz problem for the twisted Laplacian $\mathcal L$ on $\mathbb R^2$. For $p\in [1, \infty]\setminus\{2\}$, it has been conjectured that the Bochner-Riesz means $S_\lambda^\delta(\mathcal L) f$ of order $\delta$ converges in $L^p$ for every $f\in L^p$ if and only if $\delta> \max(0,|(p-2)/p|-1/2)$. We prove the conjecture by obtaining uniform $L^p$ bounds on $S_\lambda^\delta(\mathcal L)$ up to the sharp summability indices.Comment: 15 page
Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality...
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Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality...
Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality...
Let $R_{1,2}$ be scalar Riesz transforms on $\mathbb{R}^2$. We prove that the $L^p$ norms of $k$-th ...
We study Lp norm convergence of Bochner-Riesz means SδRƒ associated with certain non-negat...
AbstractWe study the Bochner–Riesz operator on weighted Lebesgue spaces and give the sharp bound for...
We obtain weak-type $(p, p)$ endpoint bounds for Bochner–Riesz means for the Hermite operator $H = -...
In the present paper we study the behaviour as p goes to 1 of the weak solutions to the problems 8 ...
In this paper, we study the $L^p(\mathbb{R}^2)$-improving bounds, i.e., $L^p(\mathbb{R}^2)\rightarro...
In this paper we study the existence of maximizers for two families of interpolation inequalities, n...
AbstractThe Bochner–Riesz means for Fourier–Bessel expansions are analyzed. We prove a uniform two-w...
In this paper we introduce Stein's square function associated with bilinear Bochner-Riesz means and ...
In this paper we establish a priori bounds for positive solution of the N-Laplace equation in a boun...
We prove an almost everywhere convergence result for Bochner–Riesz means of (Formula presented.) fun...
We consider weak solutions to a class of Dirichlet boundary value problems involving the $p$-Laplace...
We consider the equation (pu')'-qu+λwu = f in (0,1) subject to homogenous boundary conditions at x =...
Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality...
Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality...
Let $R_{1,2}$ be scalar Riesz transforms on $\mathbb{R}^2$. We prove that the $L^p$ norms of $k$-th ...