Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type

  title={Maximal functions associated with Fourier multipliers of Mikhlin-H{\"o}rmander type},
  author={Michael Christ and Loukas Grafakos and Petr Honz{\'i}k and Andreas Seeger},
  journal={Mathematische Zeitschrift},
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 multipliers under which Lp boundedness of the maximal operators holds. 

A Cotlar type maximal function associated with Fourier multipliers

  • R. Srivastava
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2020

A Marcinkiewicz maximal-multiplier theorem

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.

Maximal functions of multipliers on compact manifolds without boundary

Let $P$ be a self-adjoint positive elliptic (-pseudo) differential operator on a smooth compact manifold $M$ without boundary. In this paper, we obtain a refined $L^p$ bound of the maximal function

Maximal functions for multipliers on stratified groups

In this paper we obtain a refined Lp bound for maximal functions of the multiplier operators on stratified groups and maximal functions of the multi‐parameter multipliers on product spaces of

The space of maximal Fourier multipliers as a dual space

Figa-Talamanca characterized the space of Fourier multipliers as the dual space of a certain Banach space. In this paper, we characterize the space of maximal Fourier multipliers as a dual space

Problems on averages and lacunary maximal functions

We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First, we obtain an $H^1$ to $L^{1,\infty}$ bound for lacunary maximal

Lipschitz Linearization of the Maximal Hyperbolic Cross Multiplier

We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition and a lower bound on the linearizing function, we

$L^p$ boundedness for maximal functions associated with multi-linear pseudo-differential operators

In this paper, we establish the $L^p$ estimates for the maximal functions associated with the multilinear pseudo-differential operators. Our main result is Theorem 1.2. There are several major



Estimates nearL1 for Fourier multipliers and maximal functions

Demonstration d'une version du theoreme des multiplicateurs de Hormander. Etude de quelques operateurs maximaux

Radial Fourier Multipliers and Associated Maximal Functions

Classical and modern Fourier analysis

Prolegomena. 1. L p Spaces and Interpolation. 2. Maximal Functions, Fourier Transform, and Distributions. 3. Fourier Analysis on the Torus. 4. Singular Integrals of Convolution Type. 5.

Maximal functions and Fourier transforms

On maximal functions generated by Fourier multipliers

Hp spaces of several variables


A note on interpolation spaces

Estimates for translation invariant operators inLp spaces