Weighted boundedness of multilinear integral operators for the endpoint cases

<abstract><p>We prove the weighted boundedness for the multilinear operators associated to some integral operators for the endpoint cases. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.</p></abstract>

BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES

In an extrapolation argument, we prove certain $L^{p}\,(1<p<\infty )$ estimates for nonisotropic Marcinkiewicz operators associated to surfaces under the integral kernels given by the elliptic sphere functions ${\rm\Omega}\in L(\log ^{+}L)^{{\it\alpha}}({\rm\Sigma})$ and the radial function $h\in {\mathcal{N}}_{{\it\beta}}(\mathbb{R}^{+})$. As applications, the corresponding results for parametric Marcinkiewicz integral operators related to area integrals and Littlewood–Paley $g_{{\it\lambda}}^{\ast }$-functions are given.

Sharp maximal function estimates and boundedness for commutators associated with general integral operator

In this paper, we establish the sharp maximal function estimates for the commutator associated with some integral operator with general kernel and the weighted Lipschitz functions. As an application, we obtain the boundedness of the commutator on weighted Lebesgue, Morrey and Triebel-Lizorkin space. The operator includes Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

Continuity of Multilinear Marcinkiewicz Operators for the Extreme Cases of 𝑝

We prove the continuity properties of multilinear Marcinkiewicz operators for the extreme cases of 𝑝.

Continuity for Multilinear Marcinkiewicz Operators on Certain Hardy Spaces

In this paper, the continuity of multilinear Marcinkiewicz operators on certain Hardy and Herz–Hardy spaces is obtained.

Boundedness for multilinear Marcinkiewicz operators on certain Hardy spaces

The boundedness for the multilinear Marcinkiewicz operators on certain Hardy and Herz-Hardy spaces are obtained.