Zunwei Fu

Endpoint estimates for n-dimensional Hardy operators and their commutators

In this paper, the sharp bound for the weak-type (1, 1) inequality for the n-dimensional Hardy operator is obtained. Moreover, the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out. As applications, the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced. It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space. The endpoint estimate for the commutator generated by the Hardy operator and the (central) BMO function is also discussed.

Commutators of weighted Hardy operators on ℝⁿ

The purpose of this paper is to establish a sufficient and necessary condition on weight functions which ensures the boundedness of the commutators of weighted Hardy operators (with symbols in BMO(ℝ n )) on L P (ℝ n ), where 1 < p < ∞.

Estimates for operators on weighted Morrey spaces and their applications to nondivergence elliptic equations

In this paper, we study the norm inequalities for sublinear operators and their commutators on weighted Morrey spaces. As application, the regularity in the weighted Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients is considered.MSC:42B20, 35J25.

Weighted multilinear Hardy operators and commutators

In this paper, we introduce a type of weighted multilinear Hardy operators and obtain their sharp bounds on the product of Lebesgue spaces and central Morrey spaces. In addition, we obtain sufficient and necessary conditions of the weight functions so that the commutators of the weighted multilinear Hardy operators (with symbols in central BMO space) are bounded on the product of central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Riemann-Liouville and Weyl.

Boundedness of One-Sided Oscillatory Integral Operators on Weighted Lebesgue Spaces

We consider one-sided weight classes of Muckenhoupt type, but larger than the classical Muckenhoupt classes, and study the boundedness of one-sided oscillatory integral operators on weighted Lebesgue spaces using interpolation of operators with change of measures.

Boundedness of Sublinear Operators with Rough Kernels on Weighted Morrey Spaces

The aim of this paper is to get the boundedness of a class of sublinear operators with rough kernels on weighted Morrey spaces under generic size conditions, which are satisfied by most of the operators in classical harmonic analysis. Applications to the corresponding commutators formed by certain operators and BMO functions are also obtained.

Estimates of Some Operators on One-Sided Weighted Morrey Spaces

A version of one-sided weighted Morrey space is introduced. The boundedness of some classical one-sided operators in harmonic analysis and PDE on these spaces are discussed, including the Riemann-Liouville fractional integral.

A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝ

We introduce certain type of weighted variant of Riemann-Liouville fractional integral on ℝ𝑛 and obtain its sharp bounds on the central Morrey and 𝜆-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators (with symbols in 𝜆-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Weyl and Cesaro.

Weighted Multilinear Hardy Operators on Herz Type Spaces

This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product Morrey-Herz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions. Finally, we extend the obtained results to the product Morrey-Herz spaces.

Real interpolation of weighted tent spaces

Let and be a Muckenhoupt weight. In this article, the authors study the real interpolation of the weighted tent space . For all , , and , the authors show that , where and denotes the weighted Lorentz-tent space, which is introduced in this article. As an application, the authors prove a real interpolation result on the weighted Hardy spaces for all and , which, when , seals a gap existing in the original proof of a corresponding result of Fefferman et al. [Trans. Amer. Math. Soc. 1974;191:75–81].