9 papers · 1 filter
A sharp Hörmander estimate for multi-parameter and multi-linear Fourier multiplier operators
Jiao Chen, Danqing He, Guozhen Lu +2
In this paper, we investigate the Hörmander type theorems for the multi-linear and multi-parameter Fourier multipliers. When the multipliers are characterized by -based Sobole…
On the boundedness of multilinear Fourier multipliers on Hardy spaces
Jin Bong Lee, Bae Jun Park
In this paper, we study multilinear Fourier multiplier operators on Hardy spaces. In particular, we prove that the multilinear Fourier multiplier operator of Hörmander type is boun…
Initial bounds for multilinear operators
Loukas Grafakos, Danqing He, Petr Honzík +1
The boundedness theory of convolution operators is \linebreak based on an initial estimate derived from the Fourier transform. The corresponding theory of multil…
The multilinear Hormander multiplier theorem with a Lorentz-Sobolev condition
Loukas Grafakos, Bae Jun Park
In this article, we provide a multilinear version of the Hörmander multiplier theorem with a Lorentz-Sobolev space condition. The work is motivated by the recent result of the firs…
Characterization of multilinear multipliers in terms of Sobolev space regularity
Loukas Grafakos, Bae Jun Park
We provide necessary and sufficient conditions for multilinear multiplier operators with symbols in -based product-type Sobolev spaces uniformly over all annuli to be bounded…
On the failure of multilinear multiplier theorem with endpoint smoothness conditions
Bae Jun Park
We study a multilinear version of Hörmander multiplier theorem, namely \begin{equation*} \Vert T_σ(f_1,\dots,f_n)\Vert_{L^p}\lesssim \sup_{k\in\mathbb{Z}}{\Vert σ(2^k\cdot,\dots,2^…