We suppose that S is a smooth hypersurface in Rn+1 with Gaussian curvature re and surface measure dS, it) is a compactly supported cut-off function, and we let pa be the surface measure with dßa = u>Ka dS. In this paper we consider the case where S is the graph of a suitably convex function, homogeneous of degree d, and estimate the Fourier transform ßa. We also show that if S is convex, with n...

Given an approach region Γ ∈ Z+ and a pair U , V of commuting nonperiodic measure preserving transformations on a probability space (Ω,Σ, μ), it is shown that either the associated multiparameter ergodic averages of any function in L(Ω) converge a.e. or that, given a positive increasing function φ on [0,∞) that is o(log x) as x → ∞, there exists a function g ∈ Lφ(L) (Ω) whose associated multipa...

This is the third part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. For L in some class of elliptic operators, we study weighted norm L inequalities for singular “non-integral” operators arising from L ; those are the operators φ(L) for bounded holomorphic functions φ, the Riesz transforms ∇L−1/2 (or (−∆)1/2L−1/2) and its inverse L1/...

Normalizers and p-normalizers of maximal tori in p-compact groups can be characterized by the Euler characteristic of the associated homogeneous spaces. Applied to centralizers of elementary abelian p-groups these criteria show that the normalizer of a maximal torus of the centralizer is given by the centralizer of a preferred homomorphism to the normalizer of the maximal torus; i.e. that “norm...

In this paper we derive maximal pointwise Hölder estimates for the Kohn’s Laplacian on strongly pseudoconvex CR manifolds of class C3 using the Tanaka-Webster Pseudohermitian metric. The estimates can be used to improve the Boutet De Monvel’s embedding theorem for strongly pseudoconvex compact CR manifolds of real dimension greater or equal to five with less smoothness assumption.

We show that a maximal inequality holds for the non-tangential maximal operator on Dirichlet spaces with harmonic weights on the open unit disc. We then investigate two notions of Carleson measures on these spaces and use the maximal inequality to give characterizations of the Carleson measures in terms of an associated capacity.

In this paper we consider the vector-valued extension of the Fefferman-Stein-Stronberg sharp maximal inequality under growth condition. As an application we obtain the vectorvalued extension of the boundedness of the commutator. Furthermore we prove the boundedness of the commutator.

In analogy with the maximal tensor product of C *-algebras, we define the " maximal " tensor product E 1 ⊗ µ E 2 of two operator spaces E 1 and E 2 and we show that it can be identified completely isometrically with the sum of the two Haagerup tensor

The aim of this paper is to study semigroups possessing E-regular elements, where an element a of a semigroup S is E-regular if a has an inverse a◦ such that aa◦, a◦a lie in E ⊆ E(S). Where S possesses ‘enough’ (in a precisely defined way) E-regular elements, analogues of Green’s lemmas and even of Green’s theorem hold, where Green’s relations R,L,H and D are replaced by R̃E , L̃E , H̃E and D̃E . N...