Related papers: Lipschitz linearization of the maximal hyperbolic …

We prove the $L^p$-boundedness of the strong maximal operator defined on a Heisenberg group w.r.t an absolutely continuous measure satisfying the product $A_\infty$-property.

The main aim of this paper is to investigate $\left( H_{p},L_{p}\right) $ and $\left( H_{p},L_{p,\infty }\right) $ type inequalities for maximal operators of Riesz logarithmic means of one-dimensional Vilenkin-Fourier series.

The Hilbert transform is essentially the \textit{only} singular operator in one dimension. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on…

In this paper, we study the Lp-bondedness of the spherical maximal function associated to the Dunkl operators.

We prove $L^p\times L^q\rightarrow L^r$ bounds for certain lacunary bilinear maximal averaging operators with parameters satisfying the H\"older relation $1/p+1/q=1/r$. The boundedness region that we get contains at least the interior of…

This is a continuation of our previous research about an oscillatory integral operator $T_{\alpha, \beta}$ on compact manifolds $\mathbb{M}$. We prove the sharp $H^{p}$-$L^{p,\infty}$ boundedness on the maximal operator $T^{*}_{\alpha,…

We find necessary and sufficient conditions for the validity of weighted Rellich and Calderon-Zygmund inequalities in L^p, 1 \leq p \leq \infty, in the whole space and in the half-space with Dirichlet boundary conditions. General operators…

In this article, we characterize the bounded and the compact multiplication operators between distinct iterated logarithmic Lipschitz spaces, and between the Lipschitz space and an iterated logarithmic Lipschitz space of an infinite tree.…

In this paper, we determine the $L^p(\mathbb{R})\times L^q(\mathbb{R})\rightarrow L^r(\mathbb{R})$ boundedness of the bilinear Hilbert transform $H_{\gamma}(f,g)$ along a convex curve $\gamma$…

Let $M_{G}$ be the centered Hardy-Littlewood maximal operator on a finite graph $G$. We find $\underset{p\to \infty}{\lim}\|M_{G}\|_{p}^{p }$ when $G$ is the start graph ($S_n$) and the complete graph ($K_n$), and we fully describe…

Given a differential operator defined in terms of left-invariant vector fields on a Lie group, we prove that the local condition defining maximal hypoellipticity is equivalent to a global estimate if the operator is left invariant. As a…

A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise…

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 study the $L^p$ mapping properties of the strong spherical maximal function, which is a multiparameter generalisation of Stein's spherical maximal function. We show that this operator is bounded on $L^p$ for $p > 2$ in all dimensions $n…

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…

We develop a new approach to the invertibility of the layer potentials on $L^p$ associated with elliptic equations and systems in Lipschitz domains. As a consequence, for $n\ge 4$ and $(2(n-1)/(n+1))-\epsilon<p<2$, we obtain the solvability…

In this paper, the main aim is to consider the boundedness of the Hardy-Littlewood maximal commutator $M_{b}$ and the nonlinear commutator $[b, M]$ on the Lebesgue spaces and Morrey spaces over some stratified Lie group $\mathbb{G}$ when…

We prove the existence of an open set minimizing the first Dirichlet eigenvalue of an elliptic operator with bounded, measurable coefficients, over all open sets of a given measure. Our proof is based on a free boundary approach: we…

We derive regularity estimates for viscosity solutions to the parabolic normalized p-Laplace. By using approximation methods and scaling arguments for the normalized p-parabolic operator, we show that the gradient of bounded viscosity…

We prove the $L^p$-boundedness for all $p \in (1,\infty)$ of the first-order Riesz transforms $X_j \mathcal{L}^{-1/2}$ associated with the Laplacian $\mathcal{L} = -\sum_{j=0}^n X_j^2$ on the $ax+b$-group $G = \mathbb{R}^n \rtimes…