A Marcinkiewicz maximal-multiplier theorem

  title={A Marcinkiewicz maximal-multiplier theorem},
  author={Richard Oberlin},
For r < 2, we prove the boundedness of a maximal operator formed by applying all multipliers m with $\|m\|_{V^r} \leq 1$ to a given function. 

A Fefferman-Stein inequality for the Carleson operator

We provide a Fefferman-Stein type weighted inequality for maximally modulated Calder\'on-Zygmund operators that satisfy \textit{a priori} weak type unweighted estimates. This inequality corresponds

Maximal Marcinkiewicz multipliers

Let $\mathcal{M} =\{m_{j}\}_{j=1}^{\infty}$ be a family of Marcinkiewicz multipliers of sufficient uniform smoothness in $\mathbb{R}^{n}$. We show that the Lp norm, 1<p<∞, of the related maximal



Endpoint multiplier theorems of Marcinkiewicz type

We establish sharp (H1,L1,q) and local (L logrL,L1,q) mapping properties for rough one-dimensional multipliers. In particular, we show that the multipliers in the Marcinkiewicz multiplier theorem map

Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type

Abstract.We show that maximal operators formed by dilations of Mikhlin- Hörmander multipliers are typically not bounded on Lp(ℝd). We also give rather weak conditions in terms of the decay of such

Breaking the duality in the return times theorem

We prove Bourgain's Return Times Theorem for a range of exponents $p$ and $q$ that are outside the duality range. An oscillation result is used to prove hitherto unknown almost everywhere convergence

A variation norm Carleson theorem

By a standard approximation argument it follows that S[f ] may be meaningfully defined as a continuous function in ξ for almost every x whenever f ∈ L and the a priori bound of the theorem continues

Issues related to Rubio de Francia's Littlewood--Paley Inequality: A Survey

Rubio de Francia's Littlewood Paley inequality is an extension of the classical Littlewood Paley inequality to one that holds for a decomposition of frequency space into arbitrary disjoint intervals.

Multiplicateurs de Fourier de L p (R) et estimations quadratiques

  • C. R. Acad. Sci. Paris Sér. I Math
  • 1988