Related papers: A Marcinkiewicz maximal-multiplier theorem

The main aim of this paper is to prove that when $0<p<1/2$ the maximal operator $\overset{\sim }{\sigma }_{p}^{\ast }f:=\underset{n\in \mathbb{N}}{% \sup }\frac{\left\vert \sigma_{n}f\right\vert }{\left( n+1\right) ^{1/p-2}}$ is bounded…

We control a broad class of singular (or "rough") Fourier multipliers by geometrically-defined maximal operators via general weighted $L^2(\mathbb{R})$ norm inequalities. The multipliers involved are related to those of Coifman--Rubio de…

This work is devoted to studying the boundedness on Lebesgue spaces of bilinear multipliers on $\R$ whose symbol is narrowly supported around a curve (in the frequency plane). We are looking for the optimal decay rate (depending on the…

In this paper we derive the maximal subspace of positive numbers, for which the restricted maximal operator of Fej\'er means in this subspace is bounded from the Hardy space $H_{p}$ to the space $L_{p}$ for all $0<p\leq 1/2.$ Moreover, we…

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…

We give an extension of Rubio de Francia's extrapolation theorem for functions taking values in UMD Banach function spaces to the multilinear limited range setting. In particular we show how boundedness of an $m$-(sub)linear operator…

We extend a classical result by Triebel on boundedness of bandlimited multipliers on $L^p(\mathbb{R}^n)$, $0<p\leq 1$, to a vector-valued and matrix-weighted setting with boundedness of the bandlimited multipliers obtained on $L^p(W)$,…

In this paper we study sharp generalizations of $\dot{F}_p^{0,q}$ multiplier theorem of Mikhlin-H\"ormander type. The class of multipliers that we consider involves Herz spaces $K_u^{s,t}$. Plancherel's theorem proves…

We establish very general criteria for the existence of multiplication operators between noncommutative Orlicz spaces $L^{\psi_0}(\tM)$ and $L^{\psi_1}(\tM)$. We then show that these criteria contain existing results, before going on to…

We present a brief survey of recent results on boundedness of some classical operators within the frameworks of weighted spaces $L^{p(\cdot)}(\varrho)$ with variable exponent $p(x)$, mainly in the Euclidean setting and dwell on a new result…

Let $M$ be the Doob maximal operator on a filtered measure space and let $v$ be an $A_p$ weight with $1<p<+\infty$. We try proving that \begin{equation}\lVert M f\rVert _{L ^{p}(v) }\leq p^{\prime}[v]^{\frac{1}{p-1}}_{A_p}\lVert f\rVert _{L…

We show that the number of partitions of n with alternating sum k such that the multiplicity of each part is bounded by 2m+1 equals the number of partitions of n with k odd parts such that the multiplicity of each even part is bounded by m.…

We prove that Calder\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on…

We study the boundedness problem for maximal operators $\mathbb{M}_{\sigma}$ associated to flat plane curves with Mitigating factors, defined by $$\mathbb{M}_{\sigma}f(x) \, := \, \sup_{1 \leq t \leq 2} \left|\int_{0}^{1} f(x-t\Gamma(s)) \,…

In the present paper, we shall give a characterization for weak/strong Adams-type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces.

We obtain several sharp lower and upper bounds for the Euclidean operator radius of a pair of bounded linear operators defined on a complex Hilbert space. As applications of these bounds we deduce a chain of new bounds for the classical…

We introduce a simple sieve-theoretic approach to studying partial sums of multiplicative functions which are close to their mean value. This enables us to obtain various new results as well as strengthen existing results with new proofs.…

In this article we prove that the $n$-linear operator whose symbol is the characteristic function of the simplex $\Delta_n = \xi_1 < ... < \xi_n$ is bounded from $L^2 \times ... \times L^2$ into $L^{2/n}$, generalizing in this way our…

$L^p$ boundedness of the circular maximal function $\mathcal M_{\mathbb{H}^1}$ on the Heisenberg group $\mathbb{H}^1$ has received considerable attentions. While the problem still remains open, $L^p$ boundedness of $\mathcal…

In this paper, the author studies the boundedness for a large class of sublinear operator $T_\alpha, \alpha\in[0,n)$ generated by Calder{\'o}n-Zygmund operators ($\alpha=0$) and generated by fractional integral operator ($\alpha>0$) on…