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. 
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References

SHOWING 1-7 OF 7 REFERENCES

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.…

A Littlewood-Paley Inequality for Arbitrary Intervals

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

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