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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 Cesàro. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, the Herz spaces and the Morrey-Herz spaces. [ABSTRACT FROM AUTHOR]

This paper is primarily concerned with the proof of the L p boundedness of parabolic Littlewood-Paley operators with kernels belonging to certain block spaces. Some known results are essentially extended and improved. [ABSTRACT FROM AUTHOR]

In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral $$ \mu ^{\rho }_{{\Omega ,S}} $$ is a bounded operator from the Hardy space H 1(ℝ n ) to L 1(ℝ n ) and from the weak Hardy space H 1,∞(ℝ n ) to L 1,∞(ℝ n ), respectively. As corollaries of the above results, it is shown that $$ \mu ^{\rho }_{{\Omega ,S}} $$ is also an operator of weak type (1, 1) and of type ( p, p) for 1 < p < 2, respectively. These conclusions are substantial improvement and extension of some known results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain that a strongly singular integral operator is bounded on Lpw space for 1 < p < ∞. We also obtain that a strongly singular integral operator is a bounded operator from Hpw to Lpw for some weight w and 0 < p ≤ 1. And by an atomic decomposition, we obtain that a strongly singular integral operator is a bounded operator on Hpw for some w and 0 < p ≤ 1. [ABSTRACT FROM AUTHOR]

In this paper, we treat a class of non–standard commutators with higher order remainders in the Lipschitz spaces and give ( L p , L q ), ( H p , L q ) boundedness and the boundedness in the Triebel– Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result. [ABSTRACT FROM AUTHOR]

Let $$ B^{A}_{{\delta , * }} $$ be the maxiamal multilinear Bochner–Riesz operators generated by Bochner– Riesz operators and D α A ∈ Lip β(| α| = m). The continuity of the operator on some Hardy and Herz type Hardy is obtained. [ABSTRACT FROM AUTHOR]

In this paper, the authors study the boundedness properties of $$ \mu ^{m}_{{\Omega ,b}} $$ generated by the function b ∈ Lip β (ℝn)(0 < β ≤ 1/ m) and the Marcinkiewicz integrals operator μ Ω . The boundednesses are established on the Hardy type spaces $$ H^{p}_{{b^{m} ,s}} {\left( {\mathbb{R}^{n} } \right)} $$ and the Herz–Hardy type spaces $$ H_{{b^{m} }} \dot{K}^{{\alpha ,p}}_{q} {\left( {\mathbb{R}^{n} } \right)} $$ . [ABSTRACT FROM AUTHOR]

In this paper we consider the commutators of fractional integrals [this equation cannot be represented on ASCII text] on the Besov spaces Bs, q p, where b is a locally integrable function and 0 < α < n. We first establish the equivalence between the boundedness of the commutators and the paraproduct of J. M. Bony. Then we obtain two conditions on the boundedness of the commutators. One of these conditions is necessary and the other is sufficient. [ABSTRACT FROM AUTHOR]

Deals with weighted (L[sup p], L[sup q]) estimates for a class of multilinear oscillatory singular integrals with smooth polynomial phases. Lebesgue space; Weighted (L[sup p], L[sup q]) boundedness; Endpoint estimates.

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. [ABSTRACT FROM AUTHOR]

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$(mathbb {R}^{n})$) on $L^{p}(mathbb {R}^{n})$, where $1

The authors establish λ-central BMO estimates for commutators of singular integral operators with rough kernels on central Morrey spaces. Moreover, the boundedness of a class of multisublinear operators on the product of central Morrey spaces is discussed. As its special cases, the corresponding results of multilinear Calderón-Zygmund operators and multilinear fractional integral operators can be deduced, respectively. [ABSTRACT FROM AUTHOR]