Related papers: A Hardy-Littlewood Maximal Operator Adapted to the…

Let $M$ be a manifold with ends constructed in \cite{GS} and $\Delta$ be the Laplace-Beltrami operator on $M$. In this note, we show the weak type $(1,1)$ and $L^p$ boundedness of the Hardy-Littlewood maximal function and of the maximal…

We discuss the Hardy-Littlewood maximal operator on discrete Morrey spaces of arbitrary dimension. In particular, we obtain its boundedness on the discrete Morrey spaces using a discrete version of the Fefferman-Stein inequality. As a…

We characterize weighted modulation spaces (data space) for which the heat semigroup $e^{-tL}f$ converges pointwise to the initial data $f$ as time $t$ tends to zero. Here $L$ stands for the standard Laplacian $-\Delta $ or Hermite operator…

We show that Petermichl's dyadic operator $\mathcal{P}$ (S. Petermichl (2000), Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol) is a Calder\'{o}n-Zygmund type operator on an adequate metric normal space of…

We represent by $\{W_{\lambda, t}^\alpha\}_{t>0}$ the semigroup generated by $-\mathbb L^{\alpha}_\lambda$, where $\mathbb L^{\alpha}_\lambda$ is a Hardy operator on a half space. The operator $\mathbb L^{\alpha}_\lambda$ includes a…

Let $L$ be the generator of an analytic semigroup whose kernels satisfy Gaussian upper bounds and H\"older's continuity. Also assume that $L$ has a bounded holomorphic functional calculus on $L^2(\mathbb{R}^n)$. In this paper, we construct…

We construct ladder operators, $\tilde{C}$ and $\tilde{C^\dagger}$, for a multi-step rational extension of the harmonic oscillator on the half plane, $x\ge0$. These ladder operators connect all states of the spectrum in only…

In this paper, we establish the one-sided maximal ergodic inequalities for a large subclass of positive operators on noncommutative $L_p$-spaces for a fixed $1<p<\infty$, which particularly applies to positive isometries and general…

Dependencies of the optimal constants in strong and weak type bounds will be studied between maximal functions corresponding to the Hardy--Littlewood averaging operators over convex symmetric bodies acting on $\mathbb R^d$ and $\mathbb…

Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on $\mathbb{R}^n$ and $X$ a ball quasi-Banach function space on $\mathbb{R}^n$ satisfying some mild assumptions. Denote by…

Let $L= -\Delta_{\mathbb{H}^n}+V$ be a Schr\"odinger operator on the Heisenberg group $\mathbb{H}^n$, where $\Delta_{\mathbb{H}^n}$ is the sub-Laplacian and the nonnegative potential $V$ belongs to the reverse H\"older class…

We give a quantitative characterization of the pairs of weights $(w,v)$ for which the dyadic version of the one-sided Hardy-Littlewood maximal operator satisfies a restricted weak $(p,p)$ type inequality, for $1\leq p<\infty$. More…

In this article we characterize all possible cases that may occur in the relations between the sets of $p$ for which weak type $(p,p)$ and strong type $(p,p)$ inequalities for the Hardy--Littlewood maximal operators, both centered and…

In this paper, we study the boundedness theory for maximal Calder\'on-Zygmund operators acting on noncommutative $L_p$-spaces. Our first result is a criterion for the weak type $(1,1)$ estimate of noncommutative maximal Calder\'on-Zygmund…

We obtain an improved lower bound for the restricted reverse weak-type estimate of the Hardy-Littlewood maximal operator $M$. This result is applied to the $\lambda$-median maximal operator $m_{\lambda}$ acting on a Banach function space…

We develop a technique of proving standard estimates in the setting of Laguerre function expansions of convolution type, which works for all admissible type multi-indices $\alpha$ in this context. This generalizes a simpler method existing…

In this paper we present a proof of sharp boundedness of the discrete 1-dimensional Hardy-Littlewood nontangential maximal operator, when the parameter is in the range $[\frac{1}{3},+\infty)$. This generalizes a theorem by Bober, Carneiro,…

We define $A_{p(\cdot)}^{\rm loc}$ and show that the weighted inequality for local Hardy--Littlewood maximal operator on the Lebesgue spaces with variable exponent. This work will extend the theory of Rychkov, who developed the theory of…

In this paper we study a variant of the uncentred Hardy--Littlewood maximal operator on Damek--Ricci spaces in which balls are replaced by suitable half balls. Perhaps surprisingly, such modified maximal operator has better boundedness…

We prove the self-improvement property of the Hardy--Littlewood maximal operator on quasi-Banach lattices with the Fatou property in the setting of spaces of homogeneous type. Our result is a generalization of the boundedness criterion…