We prove sharp Lp(w) norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the Ap characteristic of w for all 1 < p <∞. This implies the same sharp inequalities for the classical Lusin area integral S(f ), the Littlewood–Paley g-function, and their continuous analogs Sψ and gψ . Also, as a corollary, we obtain sharp weighted inequalities for any conv...

We establish the L boundedness of singular integrals on product domains with rough kernels in L(logL) and are supported by subvarieties.

We prove that each positive operator from a Banach lattice E to a Banach lattice F with a disjointly strictly singular majorant is itself disjointly strictly singular provided the norm on F is order continuous. We prove as well that if S : E → E is dominated by a disjointly strictly singular operator, then S2 is disjointly strictly singular.

Models of Set Theory showing exotic behaviour at singular cardinals are usually constructed via forcing. The archetypical method is Prikry-Forcing [Pr1970], which has been generalized in various ways, as for example by Gitik and Magidor [GiMa1992]. It was observed early that Prikry generic sequences can be obtained as successive critical points in an iteration of the universe V by a normal ultr...

It is well known that the non-spiraling leaves of real analytic foliations of codimension 1 all belong to the same o-minimal structure. Naturally, the question arises of whether the same statement is true for non-oscillating trajectories of real analytic vector fields. We show, under certain assumptions, that such a trajectory generates an o-minimal and model-complete structure together with th...

Consider the space Hom(Z n , G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingulariza-tion of the generic component of Hom(Z n , G), which allows us to derive formulas for its singular and equivariant cohomology in terms of the Lie algebra of a maximal torus in G and the ...

We study the weighted boundedness of the Cauchy singular integral operator SΓ in Morrey spaces L(Γ) on curves satisfying the arc-chord condition, for a class of ”radial type” almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces L(0, ...

We consider the class of meromorphic functions whose set of singular values is bounded and for which the ω -limit set of the post singular set is a compact repeller. We show that if two simple growth conditions are satisfied, then the function is ergodic on its Julia set.