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Suppose that (X, d, µ) is a metric measure space of homogeneous type in the sense of Coifman and Weiss with a reverse doubling condition. By establishing the Littlewood-Paley characterization of Li...

The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of product Calderon–Zygmund singular integral operators introduced by Journe on the product Lipschitz spaces. The key idea used in this paper is to develop the Littlewood–Paley theory for the product spaces which includes the characterization of a special product Besov space and a density argument for the product Lipschitz spaces in the weak sense.

Let $$(\mathcal {X},\rho ,\mu )$$ be Ahlfors-1 regular metric spaces. By developing the Littlewood–Paley characterization of Lipschitz spaces over $$(\mathcal {X},\rho ,\mu )$$ and establishing a density argument in the weak sense, the authors give a necessary and sufficient condition for the boundedness of Calderon–Zygmund operators on the Lipschitz spaces.

Let $(\mathcal{X},d,\mu)$ be a geometrically doubling metric space and assume that the measure $\mu$ satisfies the upper doubling condition. In this paper, the authors, by invoking a Cotlar type inequality, show that the maximal bilinear Calderón--Zygmund operators of type $\omega(t)$ is bounded from $L^{p_{1}}(\mu)\times L^{p_{2}}(\mu)$ into $L^{p}(\mu)$ for any $p_{i}\in(1,\infty]$ and bounded from $L^{p_{1}}(\mu)\times L^{p_{2}}(\mu)$ into $L^{p,\infty}(\mu)$ for $p_{1}=1$ or $p_{2}=1$, where $p \in [1/2,\infty)$, $1/{p_{1}}+1/{p_{2}}=1/{p}$. Moreover, if $\vec{w}=(w_{1},w_{2})$ belongs to the weight class $A_{\vec{p}}^{\rho}(\mu)$, using the John-strömberg maximal operator and the John-strömberg sharp maximal operator, the authors obtain a weighted weak type estimate $L^{p_{1}}(w_{1}) \times L^{p_{1}}(w_{2}) \rightarrow L^{p,{\infty}}(v_{\vec{w}})$ for the maximal bilinear Calderón--Zygmund operators of type $\omega(t)$. By weakening the assumption of $\omega\in \mathrm{Dini}(1/2)$ into $\omega\in \mathrm{Dini}(1)$, the results obtained in this paper are substantial improvements and extensions of some known results, even on Euclidean spaces $\mathbb{R}^{n}$.

In this paper, the authors study the boundedness of multilinear fractional integrals on the product Morrey space with non-doubling measure, and investigate the Morrey boundedness properties of the multilinear commutators generated by multilinear fractional integral operators with a tuple of RBMO functions.

In this paper, we obtain the boundedness of intrinsic square functions and their commutators generated with BMO functions on generalized Morrey spaces. Our theorems extend some well-known results.

Let ( X , d , μ ) be a geometrically doubling metric spaces and the measure μ satisfy the upper doubling condition. The aim of this paper, under this assumption, is to study the boundedness of the bilinear Calderón-Zygmund operator of type ω ( t ) . As an application, we obtain the Morrey boundedness properties of the bilinear operator. MSC:42B20, 42B25, 42B35.

The authors consider the multilinear Riesz potential operator defined by , where denotes the -tuple , the nonnegative integers with , , and is a nonnegative -dimensional Borel measure. In this paper, the boundedness for the operator on the product of homogeneous Morrey-Herz spaces in nonhomogeneous setting is found.