8 papers
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^…
Sharp Hardy space estimates for multipliers
Loukas Grafakos, Bae Jun Park
We provide an improvement of Calderón and Torchinsky's version of the Hörmander multiplier theorem on Hardy spaces (), by replacing the Sobolev space …
Fourier multipliers on a vector-valued function space
Bae Jun Park
We study multiplier theorems on a vector-valued function space, which is a generalization of the results of Calderón-Torchinsky and Grafakos-He-Honzík-Nguyen, and an improvement of…