# A Marcinkiewicz maximal-multiplier theorem

@inproceedings{Oberlin2011AMM, title={A Marcinkiewicz maximal-multiplier theorem}, author={Richard Oberlin}, year={2011} }

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.

## 2 Citations

### A Fefferman-Stein inequality for the Carleson operator

- Mathematics
- 2014

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

- Mathematics
- 2014

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…

## References

SHOWING 1-7 OF 7 REFERENCES

### Endpoint multiplier theorems of Marcinkiewicz type

- Mathematics
- 2000

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…

### Breaking the duality in the return times theorem

- Mathematics
- 2006

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

- Mathematics
- 2009

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

- Mathematics
- 2003

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.…

### Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type

- Mathematics
- 2003

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…

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

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