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.

In this paper some results on the structure of finite-dimensional Lie algebras are obtained by means of the concept of maximal abelian dimension. More concretely, a sufficient condition is given for the solvability in finite-dimensional Lie algebras by using maximal abelian dimensions. Besides, a necessary condition for the nilpotency is also stated for such Lie algebras. Finally, the maximal a...

For a family of weight functions, hκ, invariant under a finite reflection group on R, analysis related to the Dunkl transform is carried out for the weighted L spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a m...

We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps W (R) × W (R) → W (R) with 1 < p, q < ∞ and r ≥ 1, boundedly and continuously. The same result holds on R when r > 1. We also investigate the almost everywhere and weak convergence under the action of the classical Hardy-Littlewood maximal operator, both in its global and local versi...

Let H ∼= R ⋉ R be the Heisenberg group and let μt be the normalized surface measure for the sphere of radius t in R. Consider the maximal function defined by Mf = supt>0 |f ∗ μt|. We prove for n ≥ 2 that M defines an operator bounded on L(H) provided that p > 2n/(2n− 1). This improves an earlier result by Nevo and Thangavelu, and the range for L boundedness is optimal. We also extend the result...

Let μ be a Borel measure on Rd which may be nondoubling. The only condition that μ must satisfy is μ(Q) ≤ c0l(Q) for any cube Q ⊂ Rd with sides parallel to the coordinate axes and for some fixed n with 0 < n ≤ d. This paper is to establish the weighted norm inequality for commutators of Calderón-Zygmund operators with RBMO(μ) functions by an estimate for a variant of the sharp maximal function ...

A " k-rule " is a sequence A = ((A n , B n) : n < ω) of pairwise disjoint sets B n , each of cardinality ≤ k and subsets A n ⊆ B n. A subset X ⊆ ω (a " real ") follows a rule A if for infinitely many n ∈ ω, X ∩ B n = A n. There are obvious cardinal invariants resulting from this definition: the least number of reals needed to follow all k-rules, s k , and the least number of k-rules without a r...

New estimates on the maximal function associated to the linear Schrödinger equation are established.

We generalize the notion of ‘diagonal’ from the class of CSL algebras to masa bimodules. We prove that a reflexive masa bimodule decomposes as a sum of two bimodules, the diagonal and a module generalizing the w*-closure of the Jacobson radical of a CSL algebra. The latter module turns out to be reflexive, a result which is new even for CSL algebras. We show that the projection onto the direct ...

In the paper we prove an extension theorem for matrices with entries in H (U) for U being a Riemann surface of a special type. One of the main components of the proof is a Grauert type theorem for “holomorphic” vector bundles defined over maximal ideal spaces of certain Banach algebras.