we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.

The best constant in the usual L norm inequality for the centered Hardy-Littlewood maximal function on R is obtained for the class of all “peak-shaped” functions. A function on the line is called “peakshaped” if it is positive and convex except at one point. The techniques we use include variational methods. AMS Classification (1991): 42B25 0. Introduction. Let (0.1) (Mf)(x) = sup δ>0 1 2δ ∫ x+δ

Following the ideas of Carleson, Garnett–Jones and Fujii, we obtain a decomposition of an arbitrary measurable function f in terms of local mean oscillations. As a main application, in the case p > n we prove a conjecture by Cruz-Uribe and Pérez about two-weight norm inequalities for singular integrals. Also we extend an inequality, due to the author, relating f and the local sharp maximal func...

Let ω be a weight satisfing Muckenhoupt’s condition A∞. In present paper the estimate of rearrangement f∗ ω(t) was obtained f∗ ω(t) ≤ 2(M λ f)ω(2t) + f∗ ω(2t) (0 < t < ∞), where f is any measurable function, M λ f is local sharp maximal function due to John [12] and Strömberg [18]. Before (Bennett, DeVore and Sharpley [3], Bagby and Kurtz [1]) the similar estimates were expressed in terms of Fe...

A new proof of a weighted norm inequality for multilinear singular integrals of Calderón-Zygmund type is presented through a more general estimate involving a sharp maximal function. An application is given to the study of certain multilinear commutators.